Hello Anne,
I also have ancestors born in Whitegate, such as my great grandpa Owen Maguire and his sister Hannah was born also in 1847. You might find info at site that holds Clonrush cemetery/graveyard data and info on the Lakyle National school (
www.clonrush.eu) where your ancestor and her siblings probably attended. It looks like there is a Joe Burke of Whitegate buried in Clonrush graveyard (
http://www.clonrush.eu/JBurke.htm). If Joe Burke's grave is indexed there, there is likely a civil death record for him. If you are lucky there might be a Roman Catholic baptism record for your Hannah Burke/Bourke at rootsireland.ie at their pay site. My Hannah's baptism was there, which listed father and mother's maiden name.
Count yourself lucky to have ancestors from co Clare due to the many great helps waiting for you from Clarelibrary.ie. Note that there Whitegate/Clonrush were in Co Galway up until 1898, so don't let that confuse you like it does me. It seems you can mostly forget that, since most records show up under County Clare.
Good luck
Tom, Seattle area, Washington, USA
