The primary reason I can think of to not turn an infant and child is that adults can essentially look the same for years without being noticed. An infant or child that wasn't growing would be more noticeable.
In the books it is clear that vampires' mental abilities increase with time. When Lestat's spirit is forced into a mortal man's body he complains how slow the mind works compared to his vampire body. An infant is going to be at a huge disadvantage though. The brain is still developing all through infancy and childhood. None of this additional development would take place. At 3 months the baby's vocal cords wouldn't be completely developed, so it probably wouldn't ever be able to talk.
Given those two limitations, I think it would probably be a feral vampire, incapable of speech or thought. It would also be incredibly dependent on whoever turned it into a vampire for a long long time (or forever).
When Claudia and Louis travel to Europe together, they find vampires in eastern Europe. wikipedia
They travel throughout eastern Europe first and do indeed encounter vampires, but these vampires appear to be nothing more than mindless animated corpses.
I believe that is what an infant vampire would be.