I applaud the doctor for checking for Celiac disease. Hopefully, that will come back negative (it is an auto-immune disease, in which you cannot eat anything--even the tiniest amount--with gluten/gliadin--wheat, rye, barley--in any shape or form. Very, very restrictive).
If the test does come back negative, that does not mean your daughter doesn't have a severe intolerance to gliadin (I, my husband, and my daughter do) or to gluten--both proteins that are found in wheat, rye, barley.
While cutting out anything made from these three grains out of the diet vastly improves symptoms, if you happen to get a "little bit" in your diet by accident, that "little bit" won't rot your gut, so to say, and cause further immune problems like it would if she had Celiac disease (out of the two problems to have, gluten/gliadin intolerance is much preferred over Celiac disease).
People can have different reactions to eating gluten/gliadin--my daughter and I both get constipated; my husband has diarrhea. Most allopathic doctors will not test for food intolerances; we had to test with a Naturopathic doctor to discover our intolerance.
The fact that your little one has been eating solids--and a lot of cereal and baked goods--points to the fact that Celiac disease and/or gluten intolerance could very well be (one) of your daughter's issues. I would seriously look into it. And if all tests come back negative--I would still do a NO GLUTEN self-test for 4 weeks and see if you notice any type of improvement at all.
Once the body has been having issues with diarrhea, and it's been long and ongoing, it's very hard for the body to quiet down and repair itself. Have you been giving your daughter a good, high quality probiotic that will help restore the microflora of her gut? I would assume she doesn't have much good microflora in her gut, if she's been having almost nonstop diarrhea.
Also, the difference between food allergies and food intolerances is that a person can eat a food (say, something with gluten/gliadin in it) and not have symptoms show up for 3 or 4 days--or maybe not even for a week or two. That's known as a delayed reaction. So say you eat a piece of gluten bread on Mon, and then don't eat another piece with gluten (maybe, say, some pizza) until Weds, then maybe you eat a muffin or a piece of cake or a sandwich on Fri or Sat--if your daughter's (is she breastfed?) body doesn't react to the fact that you ate something with gluten on Mon until Weds, then you have a cascading event of her being sick--but you didn't eat anything that should manifest in her being sick.
I would urge you to take your baby to a very good, respected, and knowledgable naturopathic doctor (one who works with pregnant moms or specializes in small children would be best) and have them test your baby for food allergies, food intolerances, heavy metal toxicity, and deficiencies in minerals, vitamins, amino acids, and enzymes. I've been there. The tests are expensive. But it was the best thing I ever did three years ago for both myself and my family.
If you don't find the answers you seek in one direction--then you need to think about going a different direction to find help. For your baby's sake, please look into alternative medicine.