Teaching doggy dancing?

You have the basics with the tricks.....sort out some music which would 'fit' with the moves and listen to it, so you can plan/design the tricks to fit in time to the music, then you need to train her 'fillers' which is 'movement' that fits the tricks together, all it is, is off lead obedience work with music playing.......it is great fun ad now very competitive and was 'born' out of Mary practicing her competitive obedience work while listening to music...then she saw agility dogs warming up using other tricks in training as at shows they banned us using warm up equipment, so she devised those one on one warm up exercises into her routine and a display of HTM was then shown at Crufts the following year

if that dog dances he will get sick

Choreography plays a very important part. Your own dance is just as important. So is music. While you dance you give her hand signals for her to do the assigned routines to match your dance. Or you do the right dance to match her routines, whichever way you want to work it. It seems easier for her if you work out a series of things that she can do and arrange them in an order that is interesting and comfortable for her. Then you work out how you dance to match that routine. Good luck!