The child will need to be brought into communion with the Catholic Church. If he is under 7 (the age of reason) then there isn't a ceremony for it, it is just recorded as a note in the church registers. If he is over 7, then he goes through RCIC. When I prepare children for it, First Communion classes make up the bulk of what they need to know, and we just give them one extra class a month throughout the FHC season (9 months) to make sure they're ready for baptism or reception into the Church.
As well as that, the priest will have to have what's known as a 'founded hope' that the child will continue to be brought up Catholic, so he may want to talk to you about your circumstances, particularly if there are no Catholic family members. And he will need to explain to you the rights and obligations of becoming a Catholic, e.g. that the child would be obliged to marry according to the rites of the Catholic Church, if he ever married, and so on.
There may well still be time to get it all done in time for FHC this year, depending on how the parish runs.
Whatever you do, don't let him go through FHC with his class without having gotten his status sorted (e.g. if the school don't check his baptismal record). That can create all kinds of confusion later on. I've got an adult in RCIA class this year who has exactly that situation. It's not her fault, it's all on the parish and school for not properly checking baptismal records, but it's still her who's left with the fallout 20 years later.