I know this as I am Catholic, too. Maybe that's why I'm afraid?
My DH family is Italian Catholic.
When I told my one SIL about this, I think I heard her praying in Italian for my DD while she was holding her!
I know that my mom 'baptized' each one of her grandchildren the first time she held them. Too funny. I don't think my brothers ever knew that. Was she a priest or a pastor? Nope, just did it on her own.
Now...we grew up in the Episcopalian church. I still attend..same church I grew up in. We were all baptized. We were all confirmed...well, I was. I think 2 of my 3 brothers were, but not sure.
All three of my children were baptized, all three have had first communion. My dd, 14, is looking at being confirmed next year. Other two kids (35, and 32 were not confirmed).
Why do I tell you all this?? Because it's a family thing. It's what I believe is the spiritually right thing to do.....for my family. You? It depends on what you believe. If you don't care either way, and don't belong to a church, then I guess it may be hypercritical to baptize your child. If any of the grandparents actively belong to a church, they may feel strongly though. You 'may' want to look into baptizing your child in a grandparents church just to make them happy.
My brother actually had his only child baptized because it was a good excuse for a big party!! And th baby would get gifts, and money!! Yep, hard to believe.
My other brother didn't have either one of his two boys baptized. But, then again, Mom took care of that on the sly. Made her feel better.
It's up to you, the parents what you want to do with your child. Baptism doesn't automatically make a child more spiritual. It's just a formality...welcoming the child into the body of Christ, as a member of the church until he/she can make those promises him/herself. There are other much more meaningful rites of passage in the church...depending on what denomination you are.
Go with what your gut tells you. If your child grows up and doesn't like your choices on his/her behalf, they can make new ones for themselves. Nothing is etched in stone. Well, there are some Jewish rites that are pretty permanant but we're not going there!