What is wrong with continuing to publish with my PhD adviser?
There's nothing “wrong” with continuing to publish with your (ex-)adviser. You have correctly identified the issue to avoid: after getting your PhD, the next step in your career is to establish yourself as an independent researcher. Thus, of course: depending on the context, publishing with your adviser might send the wrong signal!

So, you should continue to publish with her, but you should make sure that it's not 100% of your research (and publications). Another point that makes a big difference is if you can, maybe now or maybe after some time, take the lead in that collaboration.