Hi Liz,

There are three 1898 & 1899 Catherine Cain entries in Brian Lawson's index to registered births, all with second names: http://www.lawsons.ca/births/cain.html. No Cath Cains there in 1900 that I can see. Catherine Elizabeth, the daughter of John Thomas Cain & Julia Jane Comaish, was born 8 May 1899, registered Douglas.
There is also an unnamed (at the time of registration) female Cain 1898 birth in Douglas, daughter of William Henry Cain & Nellie Prebble (the 1901 census should sort that one out), and there might also have been illegitimate babies named Catherine registered under their mother's surname, but later known by the father's name.

Most of Brian's index entries end during 1900, and if your Catherine was younger than she said, she will be in the register indexes later, and most birth entries from 1900 to 1903 are not online. They can only be seen in those places I gave in my last message, and which was why I suggested making a list from the indexes over several years of all possible entries. - Say 1898 to 1903.
It shouldn't take long to look through the registration district indexes for Cath Cain and illegitimate Catherine entries over those years.
Good luck.

Sue