First, you need a baptismal font. No preference on a birdbath or a hot tub though:
10. So that baptism may clearly appear as the sacrament of the Church’s faith and of incorporation into the people of God, it should normally be celebrated in the parish church, which must have a baptismal font.
Our parish font is still on wheels. I’ll post a picture someday soon.
11. After consulting the local parish priest (pastor), the bishop may permit or direct that a baptismal font be placed in another church or public oratory within the parish boundaries. In these places, too, the right to celebrate baptism belongs ordinarily to the parish priest (pastor).
I’ve never run across any instance in which a parish’s font is at a separate location from the Church. The rite does instruct that home baptisms are out:
12. Except in case of danger of death, baptism should not be celebrated in private homes.
As are baptisms in hospitals:
13. Unless the bishop decides otherwise (see no. 11), baptism should not be celebrated in hospitals, except in cases of emergency or for some other compelling pastoral reason. But care should always be taken that the parish priest is notified and that the parents are suitably prepared beforehand.
What do you make of this curious point?
14. While the liturgy of the word is being celebrated, it is desirable that children should be taken to some other place. But provision must be made for the mothers or godmothers to attend the liturgy of the word; the children should therefore be entrusted to the care of other women.
I’d consider getting a babysitter, a teen, but I can’t ever recall when a baby has been removed from the church unless she or he was raising a ruckus.