I took baby photos before for two of my friends.
Natural light is best.
Look for good backgrounds.
If your shooting film use good portrait films like Portra 400 or Reala. Black and white is also good.
If you have a 105 macro lens use it.
The comfort of the baby takes priority. You won't get good results if they are tired or hungry or uncomfortable in their clothes (parents have a tendency to over-prepare and dress up their baby).
Always be ready to shoot. Sometimes the best photos are grab shots.
Nice shots you have, I also take some shots with my son's leg and hand 3 yrs ago.. Yup Flash light is not recommended, natural light is the best, and also need to concern about the baby's mood. When he/she in good mood, you have lots of great shots from them, so get ready with you cam from time to time, you dunno when they are happy..