This is not the proper verb to do, but an instance of the auxiliary to do, used in its emphatic nuance. Notice this is not the noun dance, but the verb to dance that comes right after. For another example that may hopefully clarify:
- I do have a shirt. → ‘I really have a shirt.’ / ‘Certainly, I have a shirt.’
The problem with this in English is that "I do dance" suggests that I dance regularly. The only correct English rendition that makes sense here is "This time I AM dancing". Not "This time I'm dancing", as that omits the positive emphasis provided by כן. Not "this time I do dance" because that just sounds weird and un-English. Not "this time I will dance" because the Hebrew sentence uses present tense. The situation could be that I refused to dance up to now, but then the DJ put on my favourite song and I leapt onto the dance floor, saying "This time I am dancing."
I agree with most of what you say, but I don’t think that “I do dance” necessarily suggests that I dance regularly. Imagine that I never dance but this time after I head for the dance floor and start dancing, my husband says in surprise, “You don’t dance!” That’s when I might reply “This time I do dance!” But I’ll grant you that “This time I AM dancing!” is what you’d more likely hear.