I'm having the same problem with my 2 y.o. son, except he's waking up at 5:00 sometimes sooner. I rang CYH, they said this was Hamish's way of letting me know he was getting enough sleep. Their suggestion was to cut down sleep times slowly rather than cutting out all together in one hit.
Hamish only has one sleep, but he slept for 3-4 hours during the day. We've had to cut him back to 2 hrs. We're trialing this for a week and if things don't improve we need to cut back to 1 1/2hrs etc..
The way the CYH nurse was speaking I would slowly cut back the morning sleep rather than the arvo one and when it get cut completely just keep her occupied with trips out etc.
Hope this helps