Before you get a second dog, you need to make sure your first dog is well-trained and understands her place in the family. I would advise waiting until the puppy is at least two years old before thinking about a second dog. Two puppies can keep each other company, it’s true, but they are also twice as effective at destroying your house and belongings. Dogs learn from one another; make sure your first dogs knows exactly what she is and is not allowed to do before you add another one.
Two dogs are twice as much time, effort, and money as one dog. You say you have trouble taking just one out for walks every day- why would you think another dog would solve this problem? Adding another dog is not going to make life easier- it’s just going to make more work for you. You can’t leave your dogs alone all day ‘because they have each other’- you need to spend time with both of them every day. I’ve seen a lot of people add a second dog ’ because the first one is so lonely’ and making huge problems for themselves. If you can’t spend adequate time with the first dog, a second dog is going to take the situation out of your control. Two dogs together, with a minimum of human interaction, are going to bond to each other more strongly than they will to you. This will create massive behavioral problems in the future. If you wait until your first dog is older, more secure in her place, and knows what’s expected of her, you won’t find that sort of trouble when you add another dog. And training a puppy is actually easier when you have an older, well-trained dog around- the more mature dog will help you out with modeling behavior and keeping the young one in line.
But 9 1/2 months old is still a baby! Your dog doesn’t completely know what she’s supposed to do yet. She needs more time and more training, and she needs to just grow up. The reason your dog loves to meet and greet other dogs is because, well, she’s a dog. She’s probably a friendly, out-going sort of dog who wants to make new friends, and is generally just curious about her environment. These are good signs. And starting at about 9 months for most dogs, they start getting bolder and more curious about their world. It’s a natural part of dog maturation. You should encourage friendly contact with lots and lots of other dogs, people, and animals at this stage. It’ll help your dog to become friendly, trustworthy, well-socialized, and self-confident.
If you’re worried about your dog being lonely during the day, maybe you could come home on lunch break to let her out for 15 minutes, or if that’s not possible, ask a trustworthy friend, family member, or neighbor. You could even hire a dog-sitter to just come by for an hour while you’re at work or school to let the dog out and play for a bit. If none of these options are possible, you could try getting up early and taking the dog for a long walk before you leave. This could tire her out and encourage her to sleep most of the day while you’re away. Don’t forget lots of safe chew toys so she can occupy herself and stay out of trouble. (Nylabones and Kongs are good; stay away from plush, latex, and rawhide.)
But getting another dog now will only increase your problems. Dogs need company, it’s true, but wait until your first dog is old enough to really appreciate it and you have the time, money, and energy to cope. Good luck!
(I’m single and have 3 dogs now, BTW- it can be done, but you have to plan for it.)