Since this little one is so young you will want to do something to prepare him for the length of time you will be able to spend handling per day. This does not include time playing on a gym or playing with toys outside of the cage. This would be physically handling. Parrots can develop behaviour problems when they are used to say being handled 3 hrs a day and it suddenly changes to for example 1 hr a day. Screaming, plucking, etc are some common ones. Don't keep a structured schedule with him. Instead if you think that it is more realistic that you will be able to handle him an hour a day most of the time then get him used to this and increase the time now and then, once or twice a week. Let him play out of his cage for the remainder of the time. I find the best thing to do is have his cage in the room that has the most family activity and when you are there let him come out and play on a gym. As for the handling do it for shorter periods of time several times a day and talk to him from across the room while he is playing on his own.
Honestly he will be fine even with a new family member in the home. The only downside is he will probably learn the sounds of the baby and duplicate them.