My DD2 is 20 months and she has only had one day sleep for quite some time now. Some days she doesn't have a day sleep at all. However my DD1 started to drop her day sleeps just before she turned 2 and then by 2 she had none at all so it seems to run in the family. They both go to bed at 6.30pm and DD2 wakes at 6.30am and DD1 at 7.30am.
I think it is worth trying, dropping her second nap. Goodluck!