This is much too early. There is no proof that putting rice cereal will help with sleep, etc, especially since it is essentially empty calories and has no real nutritional value. Also, there are studies that show that introducing solids,such as the rice cereal, too early (before 4 months) can lead to an increased chances of allergies. I know that there are lots of people who will say "But I was fine, what's the big deal?", but that doesn't mean that others are "fine". My best friend's daughter has needed an epi-pen from 18 months for peanut allergies and no one on either side has the allergy. Better safe than sorry sometimes, in my opinion.
Perhaps try giving her more formula? She may just need it. I never got why there was the "no more than 4oz" kinda rules.
good luck :)
Barbara
Mommy to Annabelle, 5/18