It’s a nice gesture to invite your priest, whether or not he can attend. What jumped out at me from your post however, and what I’m responding to, is that you’re going to wait until next month to baptize your baby. With all due respect, I would urge you to have it sooner, as soon as possible. Why would you deprive your child of sanctifying grace for one minute longer than necessary? You can still have the celebration at your daughter’s birthday party, even if the baby was baptized weeks earlier. Listen to this sermon:
audiosancto.org/sermon/20131215-The-Importance-of-Timely-Baptism.html. The priest quotes from the Catechism of the Council of Trent: “The faithful are earnestly to be exhorted to take care that their children be brought to the church, as soon as it can be done with safety, to receive solemn Baptism. Since infant children have no other means of salvation except Baptism, we may easily understand how grievously those persons sin who permit them to remain without the grace of the Sacrament longer than necessity may require, particularly at an age so tender as to be exposed to numberless dangers of death.” (
ewtn.com/library/DOCTRINE/BAPTISM.TXT)
I’m not trying to criticize you or give you a hard time. Many people are not aware of the requirement to baptize babies quickly. God bless you and congratulations on your new baby.