Is your infant a lap baby? If so, you can't get a boarding pass online. You have to check-in at the counter (or the curbside), and get a special boarding pass for the baby. If you show up at the gate and try to get on the plane without the special boarding pass for the baby, they will turn you away and make you go back through the airport to the check-in line to get one. But, I don't think you could even get through security without a boarding pass for EVERYONE in the party (including the infant).
If you have purchased a seat for the infant, then you will have a regular boarding pass for the baby (that is just like everyone else's boarding pass).
Anyway, I would try to check-in online to get those A boarding passes just in case they are limiting the preboarding people. I'm assuming you are flying SW where it does matter to get on the plane early so your family can sit together. If you are flying another airline where you have assigned seats, then it doesn't really matter if you preboard.
Oh, and btw, if your infant is a lap baby, make sure you have already called SW to tell them you have a lap baby coming. They have to have it on their itinerary before you get to the airport. If you haven't called them already, then call them right away. They will change your itinerary to say "plus infant" on it.
HTH