Important to check with your company as well. You have a genuine case and I am sure this can be smoothen out with internal processes as well. Bear in mind your Marriage Cert and your child's Birth Cert will need to be submitted for benefits..
I agree you should get a professional opinion if you are worried. In any case, your LO is probably growing well but not as "fast"as you thought. What's her birth weight and did u track her growth progress?