Dear M.,
It sounds like she might have a sensitivity/intolerance to something you're feeding her. This could be resulting in a gas buildup in her stomach, which would cause discomfort -- and moaning. Some babies even overeat when they have gas b/c the feeling of warm food in the tummy temporarily relieves the symptoms.
I recommend checking with your pediatrician and seeing if you can get a referral to a pediatric gastroenterologist.
Cows milk is the most likely trigger of gas pains for babies, but nuts, soy, eggs, and wheat can do it as well.
These kinds of sensitivities/intolerances usually aren't serious, and chances are very good she'll outgrow them, but you do want to figure out what's setting it off. Alternative practitioners, like chiropractors, also have techniques for determining the source of this kind of problem.
Hope that helps!
Mira