J.;
My 3 year old son has always been a picky eater also. I buy instant breakfast drinks and put them in his milk in the morning so he gets a few more nutrients. i also give him soy milk and he prefers it since he has gotten it from a very young age.
We take him to buffets to eat all the time to keep trying different things on him. From fruits, salads, to different meats and fish.
The doctor told me not to worry about it when he gets around 5 years old all his taste will start to increase. He told me to feed him whatever he will eat even if it is the same thing over and over. Now he is almost four and is expanding his diet and filling out just fine.
I am 54 years old and raising my grandson. My daughters never had eating issues. I find that parents worry too much. Just relax your little one will thrive in spite of us parents.
If your worried about her not getting the right things to eat maybe look into putting her on vitamin. My doctor told me that wasn't even necessary but of course I did until he started eating.
Good luck and don't worry too much.
C.