Ok, it’s clear that your correct approach isn’t working. And your GP isnt rushing to refer you, for all the good reasons that a PP has outlined.
So you need to try eliminating some foods in the short term, to identity the culprit/s. Remember it may be more that one.
Can I reassure you that no harm will come to your child if you eliminate certain foods in the short term. As a PP said, gluten is not a food group. Neither is CMP or lactose.
There are thousands if not millions of people who have lived for most of their lives without eating gluten/ cheese/ onions and they are probably healthier than the general population . If your child has a food intolerance , you will transform your her life and yours by working out what it is and seeing how you can substitute that so she is healthy and happy.
As a Pp said
There's also no evidence that gluten is an essential food group that can't safely be cut out for a few weeks to see if things improve. As long as she's still getting carbs and fibre, I think it's quite sensible to trial a GF diet for a few weeks. You can have a very healthy, balanced GF diet that includes things like brown rice, potatoes / sweet potatoes, and GF oats, bread and pasta. If it improves, talk to your GP / a dietician about getting a formal diagnosis and further dietary advice; if it doesn't, You be ruled out a possible cause without doing any harm
This is a great starting point. Based on the diet you have outlined in your OP, you could put your child on a GF diet and she wouldn’t even notice, by using GF bread / wraps / pitta and Gf pasta. I’d try 3 weeks to start off.
Personally I don’t use the Processed GF foods very much but they would be useful to you in the short term at least. Because by keeping everything else in her diet the same, you can quickly work out, for example, if it’s Wheat specially or gluten more generally that is causing the problem.
That’s hard to do if you change lots of things at once.
If that doesn’t relive her symptoms, you could try omitting other high risk foods and see if that works. Worth looking at the FODMSP stuff as she has quite a mixed diet with lots of other potential suspects, like beans, bananas, , high fibre veg, oranges .
You need to keep a very strict timed food diary for her and note any symptoms at all , when she has a BM and what it’s like. Also note her behaviours - is she excited, lethargic, scratching a lot. Note things like blotchy skin. Sleeeping well or badly . Put down everything ,
Note down everything she eats or drinks except plain water, even the juice ( in case it’s a problem with a colouring or the artificial sweeteners).
You also need to check labels for all processed foods. Many yoghurts, crisps and pasta sauces contain gluten as well as the obvious bread, biscuits and pasta. NEVER assume that a processed food will be ok.