Just so you know, Purgatory isn't a solely Catholic belief. Though it's true that Luther rejected it, other Protestant forms of Christianity do believe in a "transitional phase" between death and Heaven. One of the most famous Christians to believe this is C.S. Lewis. To quote him:
"Our souls demand Purgatory, don't they? Would in not break the heart if God said to us, 'It is true, my son, that your breath smells and your rags drip with mud and slime, but we are charitable here and no one will upbraid you with these things, nor draw away from you. Enter into the joy'? Should we not reply, 'With submission, sir, and if there is no objection, I'd rather be cleaned first.' 'It may hurt, you know' - 'Even so, sir.'"
What's her face wrote:
I have big problems trying to equate a compassionate loving God with a God that would be so unbending as to let a child's soul go to hell.
Well, no one really knows, because no one sees what happens to that child's soul. I am optimistic that God would not punish the child for a lack of understanding, though. This is why I have a big problem with doctrine that claims to know 100% what happens to unborn/young children, the retarded, or likewise, because no one can ever know. We just have to know that God is without sin, and whatever He does is right and just, and accept it (and be optimistic that His mercy will allow those who cannot accept into His glory ^^).
As for Purgatory itself, I think there will be a purification process to remove our sin nature before we enter Heaven, but it won't be in a "place"; rather, it will be an instantaneous transformation.