Early Christianity IS Catholicism
Not really. Early Christianity had more to do with Judiasm and bore little connection with the "bells, statues, and incense" nature of what Catholicism quickly became by the mid second century.
To be fair the catholic Church took a long time to take shape - at least the sort of church it is today. Irenaeus, mentioned above, was from c 170CE and he was defending the faith against Gnostics especially. This was the time when the doctrine was being formed and idea after idea was being chucked out as heresy moving towards some serious doctrine at Nicea 325CE and Chalcedon 450CE.
The 'bells and whistles' or the catholic tradition hadn't even started at the time of Ireneus. The bishops in Rome were very keen to take over the church, though, and it was through Constantine, after Nicea, that bishop of Rome got set up as a prince and not, as in the past, a servant of the people. Indeed, one can't really talk about the Roman Catholic Church until after the Photian schism of c1000CE when the Eastern Church and the Roman church split up. Either of the two has a claim to the origins of Christianity though the Vatican like to bang on about it more!