I think this is very possible, but will require lots of tinkering before the training can properly start. Personally, I just started using Learning Agents, and wrote a quick tutorial here. It’s become a bit outdated already, but at least it can help with installation and getting started.
Aside from the machine learning, I think one of the bigger challenges here is to control the limbs of a character. For this I recommend checking out control rigs, and getting familiar with those, and then have the AI system interface towards that.
Assuming you have a training setup ready, there is still the challenge of teaching the agent what dancing is, and what it isn’t. Initially, you could download a bunch of dance animations from mixamo, and try to imitate those in some way.
Also, google did a similar project once, so you could check out that for inspiration: AI Choreographer: Music Conditioned 3D Dance Generation with AIST++
I hope this helps you get started! Good luck, and feel free to reach out! 
