As with adults, there is the possibility of having a funeral liturgy outside of Mass. Same reasons as for an adult: the funeral must be on a day when no funeral Mass is permitted–a liturgical reason. A priest may be unavailable–an administrative or institutional reason. The minister and family may decide that, for whatever reason, a Mass is not preferable–the pastoral option.
Obviously, all these reasons focus on the good of the mourners and the faith community. A priest doesn’t decide not to have a funeral Mass because the deceased “was just an infant” or because the parents were unmarried sinner or such.
I refer liturgy geeks to OCF 177-203 for a brief introduction on the funeral liturgy outside of Mass, and for the rite, which looks exactly like a funeral Mass, minus the liturgy of the Eucharist. Remember that OCF 307 (as does OCF 195) provides that one can have a Communion service at this liturgy.