Baby photography is not only for newborn stage, that's for sure!
Quite often clients contact me when the baby is around 3 months and they are upset that they have "missed" an opportunity to photograph the little one. It's definitely not the case and you can have your photography session arranged at any age - each stage of development has its cute moments.
Here's my youngest little one - I promised myself to take more professional photos of the kids, not only using the phone:) It's a short version of a usual photo shoot for clients. He's 4 months now and at that age we focus on getting the smiles, eye contact, cute expressions etc.
I started as soon as he's woken up from his afternoon nap. First I took a few shots on my flokati rugs.