Whooops! I think you'll still be okay to just put the binding on. If it has a wide enough border, you could attempt to square it up again and make the edges knife-straight if you'd like. Otherwise, just put the binding on. If it's a little off-square and that bothers you, you can block it after it's completed. There are lots of instructions on this site on how to block a quilt so it's square. (I've never done it, but know it's an option.)
Congrats on getting a new kitty! :)