I haven't heard of non-baptised babies being burried outside of a cemetary since Vatican two. I even went to a funeral where someone who committed suicide (a BIG no no) was burried in a Catholic Cemetary.
BTW...anyone can baptise anyone. If a baby looks like they are not going to make it, I've known nurses to baptise the baby before they pronounce the baby dead. I've even known it to happen with stillborn babies (with the parent's permission of course).
I also know of a case where they were coding a baby. The baby wasn't going to make it (about three months old) and the parents asked for someone to baptise the baby because they hadn't had the chance. This baby was not going to make it, the doctor kept the code going so that one of the nurses could perform the baptism. As soon as she finished, the baby got his heartbeat back. He survived and thrived. You never know when you're going to see God's hand.
It used to be that you baptised your baby ASAP so that they were freed from origonal sin....now people wait as much as a year. The reason is because the whole "purgatory" thing seems to be going by the wayside.