I'm grumpy when I get woken up too!!!!!
I strongly believe never wakes a sleeping baby
My vote is let her sleep til she wants first for a week and see if that makes a difference before spending money on doctors and specialist.
Recent research has shown that sleep in children may be just as important as diet in relation to their development and cognitive abilities/ learning capacities etc. at this young age they might gain more long term benefit from sleeping than doing early morning activities.
My DD has always slept quite a bit more than her peers - she's 2.5 now and still loooooves sleep ( like me!)
She wakes at 8.30 am and I just work around it.
If she misses out on any sleep it's a disaster all round!
Good luck OP Xxx