Gluten/Casein Free Diet with a Picky Eater?

Good for you it really is the best option for her. Have you looked at websites for Autisim? Autisimspeaks.org and Easterseals.com have some great information. You can also put Autisim diet into search and find a lot of info.
My granddaughter is Autistic and my daughter has her on a modified low gluten low casin diet. She has said that she can tell when her LO, 9 yrs old, has gotten too much milk in a day. One thing to cut completely and immediently is yorgert and MSG both can cause her to become violent and have those infamous meltdowns that Autistic kids have.
Once you start a routine with the diet stick to it. She may have a period of time where she will resist eating but children won't let themselves starve. They will eat and learn to eat the food placed before them. The casin free is much easier to follow, the gluten free is much more difficult and expensive.
I met a family about a year ago who had a daughter who was seriously Autistic and although the diet is difficult to follow they ate what she could eat. The did not have any foods in their home that their daughter couldn't have.

Are her doctors recommending limiting her diet? If so, have they recommended a nutritionist?

My son is dairy/casein free for allergies, but he can eat gluten. His nutrition is great and he's very healthy. There are substitutes for everything these days.

Soy milk, yogurt and cheese are all available. All veggies and fruits are safe. Meat can provide lots of protein.

Brands like Enjoy Life are free of the top 8 major allergens and available at stores like Whole Foods, Sprouts, Henry's, Wholesome Choice, and even sometimes major supermarkets and even Target.

Well, you can try different feeding therapies offered through pediatric therapy clinics. I put my son through two different types of feeding therapy and the first time all he got out of it was that he finally learned to stab a slice of banana with a fork. The second time, he learned to eat about 3 new foods is all. When I switched doctors and expressed my sons horrible eating habits he told me to scrap the feeding therapy, it clearly wasn't a route he was taking to. So, the advice he gave me is, "bribe him". Yes, at first I was against this because all the feeding therapists teach against bribes. BUT, after my husband stepped in and basically said, "screw it! We're bribing him" and got him several toys we know he'd want, it worked. My son started trying new foods, gagged on a lot of them but as he got used to the textures he started to realize there were foods he liked. Now, 3 years later, I don't have to bribe him at all anymore, he eats TONS of different foods, has a good rounded diet and I look back and think, "why didn't I bribe him sooner?". This was just my experience that worked, it could be different for your child. So if you want to stay on the safe side, try having her evaluated at a therapy clinic for feeding issues first and see how that goes. There are different feeding therapy methods, it seems every clinic adopts their favorite which may help, it may not. GL!

Will she eat grains like rice or quinoa with chopped fruit and nuts in it?

Site for families who need recipes and such for children with autism or need to stay clear of gluten.

http://pecanbread.com/

Another very IMPORTANT one to look into is

http://bodyecology.com/autism.php

So many benefit from the Body Ecology diet and now there is support for autism. Check it out ! :)

the long list of suggestions I gave you will give your daughter the best nutrition and give her a healthy change. Too much fruit is not good for her because of the high sugar content. Apples and berries are ok in moderation.