My 2.5 year old girl has the same problem, she has now stopped sleeping during the day and will go to bed of her own accord at night when she is tired. This can be anytime between 10pm and midnight! If she goes to bed at 10pm she gets up at about 6am and if it is not until midnight then she will get up at about 8am. Different children need different amounts of sleep.
She is a very happy, jovial child. The complete reverse of my grown up daughter who was a miserable child.
Natalie is mad on drawing and painting and very good for her age. Ask her to paint a car and she draws round wheels and the outline of a car's body. Where one of her little jobs is feeding the chickens, she also loves drawing and painting them! She knows all her colours, so when told to we will use the red paint next etc. she picks out the right colour. She also knows most of the 33 letters of the Ukrainian alphabet and when asked can draw or paint them. She also takes after both mum and dad, where she loves looking through books, we are both avid readers. My wife where she is a primary school teacher and teaches small infants is very good at making learning interesting and fun for Natalie with a wide range of activities. From pastry cooking, to running around kicking or throwing balloons.
The amount of energy and running about they have at this age is amazing. She is also like all 2 to 3 year olds going through the tantrum 2's where she makes her displeasure well known as soon as things aren't going how she wants them, especially when pushing the boundaries of behaviour. But around 3 they grow out of the tantrums.