Thanks for all to the input.
To Mat4mel, regarding her symptoms that match those for celiac, she has been extremely constipated ever since she started solid foods, though I've come to realize that has more to do with her refusing to drink a lot of fluids, and the iron supplements we've been giving her since her iron levels dropped several months ago. We took her off the iron at the same time we stopped the gluten, and she became regular almost immediately. But now, 2 1/2 weeks after we stopped all gluten, we put her back on the iron, and she's locked right up again. So no more iron.
The other symptoms she has are a big belly while being super-skinny, waking up in pain in the night for no apparent reason, and having very little interest in eating (since babies with celiac are often in a lot of pain, and thus don't want to hurt themselves more with food). We also thought the celiac explained the anemia, since the small intestines don't absorb nutrients when people with celiac consume gluten.
But we're finding that these symptoms can fit lots of different ailments, so we're still trying to figure it all out.
Vegmom--congratulations on your daughter bouncing back! (Although I would be over the moon to even get her up to 19 pounds by 19 months.) It seems that the problem is not parasites. They tested her stool for that last week and found nothing. Unlike your daughter, she doesn't eat much at all. It seems like I try every food under the sun with her, and she's just not interested in most of it. I'm very aware of not making it into a power struggle with her--dh and I cheerfully withdraw every food she says no to, without making a big deal of it. We just try to provide her with a wide array of food to eat throughout the whole day. But just when we think we've found something she's crazy about, she decides she no longer likes it. And the allergies she has to so many foods make it that much more difficult. That's the reason we're interested in the nutritionist coming in at this point, just to see if she can give us any fresh ideas about what to feed dd. I like the idea of a naturopath as well, though. I'm about through with traditional medicine and doctors.
I'm definitely going to try the jarrodophilus as well. I've been reading a lot of old posts on here about it, and it seems like it could really help her.
Again, thanks to everyone for the helpful comments.