Hello from Australia

I am sorry I can't help you - but thought you may be able to point me in the 'right' direction'
I am looking for the birth of William Hamilton born 1840-1845 in Gibraltar to parents Private William Hamilton and Margaret Hamilton nee Elliot.
I have checked the India Record Office and tried online the National Archives as his father was serving at some stage with the 44th Regiment of Foot but have not had any luck so far.

Regards Kay