Oh, and Perry Bible Fellowship
How about Faux Pas? Its main characters are foxes, but it has a lot of cats in it, too, and various other animals. It’s family-friendly, funny, and there’s over 2100 strips right now, most of them in a three-panel form. It has a strong continuity.
I’m glad you’ve gotten into The Order of the Stick. I second the recommendation of Gunnerkrigg Court.
I, personally, like Questionable Content but I wouldn’t rate it as being appropriate for younger readers. I’d rate it at PG-13. In addition, it takes awhile to find its legs; the first few hundred strips concentrate pretty heavily on indie music. If that’s not your genre, you probably won’t understand some of the punch lines.
And by the time it gets good, there’s a lot of premarital sex and heavy swearing. Anyway, I like it, but I wouldn’t read it to a 7-year-old, for example.
Not really for kids. Sorry… didn’t read your post closely
For one that’s light on science, but with a good amount of whimsy and wierdness, and plenty of cats (well, jut one, really):
A wrapped up set of stories Buck Godot is usually good for a reread every couple of years. You may want to preread it. I don’t remember too much that would be young teen inappropriate but I’m a 40+ year old guy who hasn’t reread it recently.
One of the McGuffins in a later arc is based on the authors childs toy so I suspect it is fairly family friendly.
Cheers,
-DF
Whoa. By the time you finish with OOTS, Breaking Cat News will probably have merch.
Oh, well. Have a blast, you two! 
You ain’t boopin’ KIDDING…
But speaking of which, PartiallyClips is pretty funny.
Uhh, yeah, no. There’s an entire arc dedicated to Buck investigating Why a bordello’s traffic has suddenly dropped precipitously.
But maybe if you pre-read, you’ll know which arcs to skip.
I recently became a fan of Scenes From a Multiverse. Maybe not for the kid, but the parental unit deserves some “me” time, too, wot?
A thousand comics or so? I’m calling that about two months work…
Which is why I’m glad to have lots of recommends!
A Miracle of Science is a good, finished webcomic set in a world where Mad Science is a genuine mental disorder and Mars is a friendly group-mind. The first chapter is black-and-white but the rest is in color.
Thank you for this recommendation! I love it.
One of my favorites is Blindsprings which is about a magical princess in a strange world. It hasn’t been updated in a while, but it’s still worth reading the archives.
I also enjoy Goblins. It had a long hiatus, but it updates regularly now, if infrequently.
Goblins does have some installments about torture, and its ugly psychological after-effects. Decide for yourself whether your kid can handle that.