Eating lunch late..

I was wondering what time your lo eats lunch. My daughter gets up around 730 and wants to eat right away... She snacks so even her breakfast isnt really a huge meal.. Maybe a bowl of fruit and she will snack on cheerios through out the morning. She then is ready to nap around 1030/11. I've tried pushing her nap to later but she's the type who will tell me and go lay down. Ive also tried giving her lunch around 1130 so she has a full belly and gets a better nap... But she wont eat if she's tired. So she takes a nap and then eats sometimes as late as 1:30/2. She then eats a snack around 330 and then dinner around 6. She goes to bed around 8. Any idead to get her to hold off on a nap and eat lunch before. Her older brothers are back in school and now I want to get her on a better schedule.