Sounds like a pretty healthy diet to me, at least for starters! But I do understand why you're stressed about it. One of mine was very fussy and still is to some extent. I became very frustrated about it initially when he was about 2 and refusing lots of foods, always picking his sandwiches apart, etc. But I could sense that I had a power struggle on my hands so decided to set some clear boundaries. I kept cooking him and his brother different things that I suspected he'd like if he tried it (i.e. not too complicated) and put it in front of him. He could choose whether or not to eat it, but if he didn't I'd make it clear that there'd be no dessert and no more food until the next meal (except fruit snacks and water of course if he needed it). I tried very hard not to be angry or negative, but just say in a neutral tone that this is dinner and if you don't want it it that's OK, but there won't be anything else to eat until breakfast, etc.
I know this sounds harsh but it worked. I did it consistently ever since and after some long battles at the dinner table, tears and tantrums and desperately hungry mornings when he hadn't eaten his dinner, he now eats nearly everything, although it can still take ages. It does help that he has a sweet tooth so I can tempt him with nice desserts. I'm not saying this approach will work for everyone, but it certainly did with us. Giving small portions to start with is key so it's easier for them to eat it all up.
Like purepurple says I think this is very common and a lot of it boils down to control. Kids can sense that we desperately want them to eat, and therefore claim some control over their lives by saying no. The harder we push, the more they refuse. I also believe fussy eaters are created, not born. A lot of kids get away with being extremely fussy because their parents find it easier to go along with it than to challenge it.
So I think it's worthwhile trying to expand your daughter's horizons a bit but without forcing it or being punitive. Talk about it with her in a calm way and explain why you'd like her to eat more things. Why doesn't she want to? Listen to what she says. Explore the market for books aimed at fussy eaters. (When my other son had issues with pooing on the loo it was a book about a boy who had the same problem I found on Amazon that cracked it.) Read books about food together at the library or choose something from a recipe book that you can make together. Involve her in cooking as much as possible and encourage her to try new things. Make faces out of food and have fun eating the monster's eye, teeth, etc. Use her favourite things as ingredients in new recipes. Invite friends over for tea - kids love sharing meals together. Give her stars on a chart for trying new things and explain why it's important to eat lots of different things (it makes you grow up to be strong and clever, etc). Take her food shopping and talk about the stuff you are buying - what it looks like and smells like and what you can make with it. If you make it fun it could take the pressure out of the whole situation.