Hi Kate, As you know there were two George Renshaws born close in age and in Ashbourne registration District. Ashbourne Sept1/4 1845 V 20 p 362 Ashbourne March1/41846 v 19 p 397 Both these Georges had mothers called Mary & both mothers, it seems, were subsequently widowed. 'My' George Renshaw, the son of Job Renshaw & Mary nee Haynes was baptised on 15th Feb 1846 atMiddleton-by-Wirksworth.
I beleive the other George Renshaw ie yours, was baptised at St Oswalds Church, Ashbourne. This church is situated on the west side of Ashbourne. It might be worth looking for a marriage between George Renshaw & Mary Clark(e)in a nearby Parish. Also Derbyshire Records Office may have records for Ashbourne Workhouse admissions.
The 1851 census lists (as far as I can tell)one George Renshaw, mother Mary Renshaw (widow). This would seem probably to refer to 'my' George Renshaw, judging by the location. I think Job died in 1851 (don't know when though). if so then perhaps your George & his mother would have emigrated before spring 1851. Best wishes elizabeth