Congratulations on getting Bassetized. From the information you provided, it's impossible to guess her age--did her former owners get her as a young pup? I'd ask your vet about that. As for the questions about getting the cats and dog used to each other, here's what I do: I used dog gates to prevent my dogs from getting into the bedroom end of the house. My dogs are so gate-shy that I can lean a gate against the door jamb, with enough of a gap at the bottom that my cat can get through. (Or if it's a fixed gate, just put it up high enough that the cat can squeeze underneath.) That way the cat can dictate how much time he wants to spend with the dogs. Luckily, my cat now LOVES my dogs, and vice versa. But there are many times that he needs to get away from them for a while. I feed the cat and keep his litterbox outside the dogs' area to prevent them from eating his food and poop. Everyone who visits my house can't understand why I have the gates set up like I do, but it works like a charm for my little menagerie!
Hope this helps. Good luck.
Hope this helps. Good luck.