Checked the record for the Presbertyrian Church in Brampton and your hunch may be correct. There were two baptisms for a Thomasine, but both with the same parent:
20th January 1810 Thomasine daughter of James Martin of Beckside.
9th March 1811, Thomasine daughter of James Martin of Beckside. It looks like Thomasine (1810 died as a baby)
The were some other baptisms that have a little more information:
18th Novemember 1804 Jennet (this could have read Janet and at a push Isabella)to James Martin, weaver of Beckside and his wife Nancy Allen.
19th January 1806 James son of James, Beckside and his wife Nancy Allen.
2nd April 1817 Margaret (aged about 2) and Helen on the same day.
I also checked the record that Robbiesmum suggested in 1832 for Thomas:
14th November 1832 Thomas Martin, illegimate son of Thomasine Martin, Buckside (or Beckside), spinster.
This seems to fit with the address.
I also see from the census record you saw for William and his daughter Thomasine that their address was Beckside, so this could be Thomasine's brother as Robbiesmum suggested. There may have been baptisms that I missed or didnt notice, so I can recheck for a baptism for William in 1808/09.
If Thomasine's daughter was called Ann, this could fit with Thomasine's mother being Nancy, pet name for Ann.
J
