You don't mention how early your daughter is getting up in the morning...maybe you can give her a later bedtime?
We're in a similar situation (my husband routinely has insomnia and will be awake until 4am or 5am and our 22 month old daughter usually wakes up somewhere between 6am and 7am). However, our daughter REFUSES to come into our bed...once she's up, she's ready to go play or whatever.
I'm just entering my 3rd trimester and have a hard time lifting her out of her crib so I make my husband go get her. :) However, I'll usually take her to the living room and let her play while I rest on the couch and daddy goes back to bed (with the knowledge that I expect him to help in an hour or two). Of course, this only works on the weekends. On weekdays when we have to get ready for work, all bets are off. If she wakes up anytime after 6am, we just get up and get ready for the day.
Is there a chair in her room where you or your husband can rest while she plays? Maybe that way she can get used to playing in her room for a while in the mornings.
Oh, and our daughter won't eat right when she wakes up, but she does usually want something to drink....