Well, this is not 100% correct - weren't both Mary and Jesus born without the stain of "original sin"?
Wikipedia:
The Immaculate Conception is, according to Roman Catholic dogma, the conception of Mary, the mother of Jesus without any stain of original sin, in her mother's womb: the dogma thus says that, from the first moment of her existence, she was preserved by God from the lack of sanctifying grace that afflicts mankind, and that she was instead filled with divine grace. Since according to Catholic doctrine man is born with the sin of Adam and therefore co-guilty, even infants need to be baptized. The Roman Catholic Church considers baptism, even for infants, so important that "parents are obliged to see that their infants are baptised within the first few weeks" and, "if the infant is in danger of death, it is to be baptised without any delay." but yet The Church has no official teaching regarding the fate of infants who die without Baptism, and theologians of the Church hold various views (for instance, some have asserted that they go to Limbo, which has never been official Catholic doctrine). "The Church entrusts these infants to the mercy of God." (Wikipedia infant baptism)
...and yet surely the dead infants have never believed that Jesus was the Son of God and that he died on the cross for their (yet to be committed) sins and hence never accepted Jesus as their personal Saviour. Didn't these infants die outside the realm of Christianity but for infant baptism?