In about a month, my husband and I are going on a two-week trip to Alaska, where we’ve never been before. The plan is to rent a camper and drive around sightseeing. Do you think we will need a gun to be safe from wildlife we might encounter?
Also keep in mind, we don’t know dick about guns and don’t have a lot of time to learn.
No.
Just what kind of wildlife were you expecting to encounter? In a RV? If a moose steps onto the road in front of you a gun isn’t going to help. Bears aren’t a problem unless you get into their territory and act stupid. Treat the trip just like one you would take in Yosemite or Yellowstone and you’ll be fine.
It’s not as bad as Florida.
Since you don’t know dick about guns, and don’t have the time for the proper safety courses etc… Just get a can of bear spray and some bangers if you want. You should be fine. When I camp in provincial parks where firearms aren’t allowed I pack bear spray with me. Never had to use it yet. Your chances of a dangerous wildlife encounter are pretty slim, you probably have a higher chance of a car accident on the way to the park.
Ah good. I only want to pet those bears, so we should be fine. 
As you can probably tell, I really don’t want to shoot anything.
Don’t go Halibut fishing without a gun. .
As for bears, the locals will give you good advice concerning where to go and how to act. Basically, make enough noise that they hear you before you see them.
Most halibut charters pack a .410 shotgun to take out the fish.
There is little chance of you running into animals at a rest stop if they handle waste right. There is more of a danger of running into moose while you are driving, so be careful and have fun!
If you don’t know dick about guns and don’t have time to learn then the answer to your question is no. I recommend bear spray if you’re concerned about animals.
No one who doesn’t know dick about guns should handle a gun, ever.
You’ll be just fine without it, and likely just fine without pepper spray or anything else. I’m sure the countless others who have made the same trip as you unarmed were just fine.
I think the need for a gun while halibut fishing is overblown by the charter industry to make it seem more dangerous/exciting for their clients.
In my work as an observer I’ve seen my share of 300 lb halibut, and I’ve never seen a commercial fisherman use a gun, or even keep one handy just in case. An aluminum t-ball bat to the snout is all you need to convince even the largest halibut to relax.
This brings to mind that old joke - they recommend that you wear bells so the bears hear you coming, and carry pepper spray so you can spray a bear if you surprise each other. You can tell grizzly bear scat from brown bear scat because it has bells in it, and it smells like pepper. 
Living as close as we do to the Rockies, people here camp and hike in the mountains all the time. Bringing guns with us is never a consideration; like everyone else has said, some bear spray might be a good idea, pay attention to signs that indicate there’s a bear in the area, stay on the trails, watch out for wildlife on the road, and have fun!
Early 70’s
Sleeping in the shell camper on the back of our pickup. ( we were poor )
No food out of the truck top even eat.
No fire made.
BIG bear came around about 1AM. Circles several times, shouldere3d the truck three time, ( scaring the wife & kids muchly, was hard to keep them quiet )
We just stayed in the truck and the bear went away.
Had we been in a tent, not so sure about events.
I do know dick about guns & was carrying a 357 Mag revolver that trip.
Did not use it.
I asked this question about our honeymoon cruise to Alaska, and Holland America told me no. Good thing, too, because there was a guy in a bear suit waving at us when we arrived in Juneau, and I totally would have gone off on him.
ETA: Instead, I just waved my arms and flapped my coat to look big and frighten him away, and, sure enough, that seemed to work.
Forget pepper spray; by the time the bear is close enough for it to be effective, you’re likely going to be a good candidate for bear scat. Buy a couple of those air horn canisters, or go to Radio Shack and get a couple of those “personal alarms” that shriek when you pull the lanyard. Bears really hate new noises in their environment and will usually run when they hear them. With the air horn, if you’re walking in at area where there is a lot of undergrowth, give it a blast every so often. I talked with a naturalist in Turnagain Pass who had never carried anything other than a personal alarm in the twenty years she’s been working in bear country. She said that every bear she had to use it for turned tail and disappeared over the next hill.
Oh, and bear bells don’t work. They make just enough noise that a bear will want to investigate. You may as well be wearing a dinner bell. If you’re in an RV, make sure you dump your food scraps both the morning after breakfast and at night before you go to bed. An RV won’t stop a grizzly, which can tear through a cabin wall without effort.
As for a gun, you would need a 12 gauge with slugs to stop a grizzly (or a very large bore pistol), assuming you could hit it in the first place while you’re hyperventilating, adrenaline is pumping, your heart is pounding like a jackhammer, and 600 pounds of fury is coming at you at 30 mph. It’s a bad idea.
Where are you going to be visiting?
Important point: Bear spray is not like bug spray. Do not attempt to repel bears by spraying it on yourself before you go in the woods.
Also, if you are hiking and get treed by a bear, the way to tell if it is a grizzly or black bear: a black bear will climb the tree after you, while the grizzly will push the tree over. 
We’ll be starting in Anchorage and plan to go to Denali, but the rest of the itinerary is not yet known.
Thanks everyone for your answers…some of them were reassuring.
There are some very cool things between the two, if you are interested in suggestions. And of course there is the other direction, down the Kenai Peninsula.
Without extensive experience in the use and care of firearms,OP, it would be ill-advised for you to take along a firearm when you travel. You are more likely to injure or kill yourself or a loved one than you are to defend yourself against the remote possibility of an animal attack.
There’s also the pesky problem of taking a firearm through Canada or on a flight. Since it would require reams of paperwork and might cause numerous issues (for instance, a handgun would be more problematic than a rifle or a shotgun.) I would suggest simply avoiding it.
From my brief sojourns in Alaska, the greatest danger would likely be your encounters with two-legged animals who are poaching or who doing something else illicit away from the cities and towns. If you stop at a local gas station, ask the people there if there have been any problems. Most will be happy to help you avoid what may be areas with “troubles.”
Have a safe trip.
I’m all ears!