I would try the route of a plant-derived iron supplement that you can find at your local co-op store, a community pharamacy, or whatever other type health food store's in your area (if they don't carry it, they might be able to order it for you).
I know you are tight on money, but you might want to seriously think about finding a naturopathic doctor and taking your daughter to see him. They know about Celiac disease/gluten intolerance and about how the body needs to have supplementation because the body isn't/won't be getting it with the gluten-free foods out there (they aren't full of added supplements like foods found in a grocery store/non-gluten foods are). They can tell you what you should be supplementing and what foods/combinations will give you "complete nutrition" for your little one. I think I've said before that giving her a Vitamin B Complex supplement for little ones would be one of the best ways to make sure she is getting everything her body needs.
Severe constipation, if it's not taken care of, can devolve into other colon issues, some of them pretty bad and life-long. Does your daughter drink water all day long (I know you've stated before that she doesn't like any of the milk alternatives)? In order to keep the colon nicely moving, water is needed for lubrication.
Also, have you tried giving her CALM, a magnesium supplement that will gently force a bowel movement? You can buy it in different flavors and mix it in water or in juice for her to drink. Since she is so constipated, you might have to give it to her for a while. It is completely natural, and you can't "overtake" the product. It is also nonaddictive. My daughter uses it once in a while (we have gluten intolerance) and it works every time; she has a nice, normal, calm BM. Once in a while, she'll also get a fissure, depending on how long it's been since she was able to eliminate. Once you get a fissure, they don't usually ever go away. There's always the risk that whenever you have issues with constipation/straining again, they can reopen. I know; I have one. Am wrestling right now with a reopened fissure.
Since you're already giving your daughter lots of foods that are usually seen as foods that help get the bowels moving and eliminating, I would seriously urge you to take your daughter to a naturopathic doctor for a full check up in terms of other foods she might be allergic or intolerant to. The body usually reacts one of two ways to a food it doesn't like: diarrhea or constipation. Since this has been going on for so long already, I would seek a second opinion from someone who is NOT in the allopathic healthcare community.
I have a strong aversion to using pharma drugs and would try anything other than using them in someone so small. My daughter took lots and lots of pharma drugs when she was little for a variety of issues/problems (we didn't catch her gluten intolerance until she was 7 years old, and I didn't open my eyes to the dangers and damages of pharma drugs until then as well), and we're still working on fixing the damage all those drugs did to her body. I know it costs more to go the natural way, but the natural way is in better alignment with the way the body really works.
Good luck.