Before my little girl went gluten-free, she was awake and crying often. After I found out that she had Celiac, I assumed that she was crying from pain in her little GI tract. It would make sense though, that she may have bad dreams because she's not feeling well, and she's not feeling well due to the gluten.
My little girl was diagnosed with Celiac (and failure to thrive) at 12 months. It took her a couple of months of gluten-freedom in order to gain weight (I think her little intestines needed time to heal before she could gain weight), but within days, she was noticeably different in terms of energy, regular BMs, and sleeping much less-which was good because when she was sick, she slept all of the time.