Just to clarify a few things-
The 1840`s was the time of the famine in Ireland, could you trace any of Kate`s family emigrating to America for instance. The Ellis Island records which are free online give the place of origin of the emigrants.
Ellis Island opened in 1892 and the online records at
www.ellisisland.org cover 1892-1924.
Earlier New York passenger arrivals are at
www.castlegarden.org but give only minimal details (name, age, occupation, country of origin)
Irish civil records are online but unless you track down the area it is going to be hard to narrow down any information and discover which family is yours.
Civil registration of births, deaths and Catholic marriages in Ireland started in 1864 (from 1845 for other marriages).
I have never been able to track down a birth entry for her or any details on her father Thomas in England. I even sent off for a birth certificate for the only Kate Hurley registered between 1842 and 1844 in the St pancras area but this turned out to be another Kate with a different father and can be traced through the census so I know it was definately not my Kate.
If Kate was born in Ireland her birth will not have been registered in England.
Note: just about to post this reply and see that census records do
not give Kate's birthplace as Ireland so there's really no point searching there until you can find more details in England. To search in Ireland you need to know where the family lived (parish if not actual townland not just the county).