C.H.
Our daughter has milk and wheat allergies. Here is what her doctor recommended, which worked for us. Pick the root foods first - sweet potatoes, carrots, etc. Make one a week. Give it to her everyday and monitor her for reactions. It feels too slow as a parent who wants to see her child eat everything, but it worked for us. After the root veggies, then start with a few fruits.
I don't know if you are going to buy the food in the market or make it yourself, so I just want to suggest making it yourself if you are open to such a task. Because of our daughter's allergies I wanted to know what was in her food and I feel an incredible sense of satisfaction doing it. Every few weeks to a month I cook for a few hours preparing her food. The food is then frozen into ice cube trays. When frozen they are stored in labeled zip-lock freezer backs.
I bought a book on making the food, but really you could just make what you are having for dinner for her too. That's up to you.
With the milk allergy, family members pressured me to try to give our daughter dairy to see if she could handle it. Our doctor advised us NOT to do this. She told us that babies with milk allergies might tolerate milk later in their little lives and that the allergy will then present itself in ear infections, for instance. We talked about how her "gut" is sensitive and needs time to heal from the few months she did have milk and wheat in it. We also give her a probiotic once a day called Flora Baby. The powder goes into her food and keeps her gut healthy.
Good luck with your quest. You can do it and be dilgent with what YOU want to feed your child.