BIG HUGS Laura
I would try pushing through. If it doesn't work within a couple of weeks, then I'd add the nap.
It took about 3 weeks (mind you there are 2 of them), granted we were travelling and out and about so they often had a catnap in the van. And sometimes that catnap seems to throw a wrench into things. After 3 weeks, it was sooooo much better. Very similar to the 2-1. There's days where they really could use the nap come early afternoon, but I just get them to bed earlier (7 vs 730). If they do catnap, they go down at 8 to save my sanity.
The first couple of weeks really are the roughest because you have no time to recoup and they are OT for days on end. Then all of a suddeen it got better. It's now 5 weeks and they cruise through the day with no nap unless they're in the van and happily go to bed at 7-730, which they haven't done in over a year. They do get some quiet time but that's on the couch watching a quiet tv program. Sometimes they doze off, but if I put them in their beds they sleep so soundly and once we couldn't even rouse D for over an hour.
I have a couple of friends who did it with no issues within a week but their children are more of the textbook/angel kind. I really think that temperment plays a part in this. More active toddlers I'm going to guess are going to have a bigger challenge with the transition. Or perhaps it's us Mummies of active toddlers who seem to get even less of a break
Big HUGS again