5-month old not developing well ...

Some background: she was a big baby (9 lbs at birth) and was developing well until 3 months when she got severe eczema and was diagnosed with pretty much all the food allergies. We now have it under control more or less.

My 5-month old doesn't seem to be developing well for her age. She hates tummy time and has weak neck control - she can keep her head up well but will lose interest and flop her head over. She likes grasping toys but won't reach for them most of the time. She giggles and coos and loves interacting with people but hasn't really belly laughed yet. She also hasn't yet rolled either direction.

She does recognize her caretakers well. She likes sitting when being held and can sit with assistance. She can "talk" and hold conversations, sometimes mimicking. She also loves sucking on her fists and has started blowing raspberries and drooling.

Her pedi said it's okay for now but being a first time mom, I'm obviously concerned.