6 year old never stops eating!!

My daughter just came out of her room. Mind you it is 3am where I live. I said you need to go back to bed and she starts ballin and says I'm hungry we haven't eaten yet. They ate a late dinner, like 11pm late cause we didn't get home till almost 1030. Anyway she had two pretty decent sized pieces of chicken, 2 servings of Mac and cheese and 2 servings of corn. Not to mention a Jr burger wacky pack meal with Apple juice and banana from sonic around .... 4?! Plus half a tray of veggies (sugar snap peas, broccoli, carrots, and celery) and some fruit today. That's just from 1pm on. We try to keep healthy food in the house and per the Dr she eats every 2-3 hours weather it's a few strawberries or breakfast lunch and dinner. I don't get how she is soooo hungry she wakes up at 3AM to eat .... But now I know she's the reason food is disappearing. What the heck do I do?!?! The dr said to give her one plate of food at meals plus like I said snacks as long as they are healthy and than cut her off but how do I cut her off if she is sneaking into the kitchen when were all sleeping?!? (16 weeks prego and unable to sleep but I'm usually knocked out this late) HELP!!!