Dianne,
I think it unlikely that someone from a farming background in Tyrone would have known a lady from Kildare, about 150 miles away. They might have met en route of course, but I’d be surprised if they knew each other in Ireland.
The tithe applotment records list most farmers in Ireland. I have gone through the records and extracted those for Co. Tyrone c 1833. (You will see some that include Fermanagh. That is because the parish of Aghalurcher straddles the two counties. I have removed those whose townlands are in Fermanagh).
Hall, Robert-Townland: Screen Y: 1827-Donacavey-Tyrone
Hall, Robert-Townland: Alderwood Year: 1833-Aghalurcher-Tyrone
Hall, Robert-Townland: Claudy Year: 1828-Cumber Upper-Tyrone
Hall, Robert-Townland: Drumwha Year: 1833-Aghalurcher-Tyrone and Fermanagh
Hall, Robert-Townland: Rehack Glebe Year: 1833-Aghalurcher-Tyrone and Fermanagh
Hall, Robert-Townland: Surcarr Year: 1833-Aghalurcher-Tyrone and Fermanagh
We can assume he was alive in 1833 if he had a son born c 1838 so he may well be one of the 6 farmers listed above. You could employ a researcher to go through the church records looking for Robert & Williamina’s marriage and William’s baptism. Not all church records have survived but there are copies of most surviving ones in PRONI in Belfast. The names all appear to fall into just 3 parishes, so not an impossible task. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
You could also go through all the Robert Hall deaths in Tyrone post 1864 in case you find one that might fit. (They’d be registered in either Armagh, Clogher, Dungannon, Irvinestown, Omagh, Cookstown, Enniskillen, Castlederg, Strabane or Gortin).