M.B.
I wouldn't touch the nap - sacred at my house! Also, overtired kids just don't sleep well.
I would put up a gate on the door to her room and tell her that if she wakes up early she can play quietly. Tell her when it's morning, you will take the gate down so that she knows when she can come get you, etc. Then get a new toy and put it in her room after she is asleep and where she will see it on her way to the door. Mr Potato Head was what we used. My almost 4 year old still asks if it's morning yet.