This John Hamilton? If so, then I can make a couple of suggestions for your research.
The obituary states that he and his wife had a number of children. I have broken through some of my ancestral brick walls by looking at each of their children and their spouses, rather than focusing strictly on my personal ancestors.
If you can find a land grant for their farm, the petition may contain a lot of genealogical information The petitions and grants are indexed online, but you need to visit the NB Archives in Fredericton to view the microfilm. The archives also have probate and other interesting records that are not yet online.
Your grave marker leads to Rhoda Estabrooks, you may want to check for a typo in the reference #.
The 1851 Census: http://www.bac-lac.gc.ca/eng/census/1851/Pages/item.aspx?itemid=611401 gives a different birth date for John, and suggests that his wife was alive in 1851. So some of the information in your tree may need to be taken with a grain of salt. For instance, the age given in his obituary may have been a guess, and his wife may have been Anna in some records, as this was often used interchangeably with Hannah.
I've also had good luck with brick walls at that time period by examining the New England Planters and Loyalists who were the first settlers of Atlantic Canada, and work forwards in time to see if you can find a son, or grandson, named John A. For example, a New England Planter named Jonathan Hamilton went to Horton, now Wolfville, NS, and he had a son named Samuel. Jonathan might be a little old to be your ancestor's father, but the pattern in family names might be a clue. And there are several NB Hamiltons listed in the Loyalist directory that you could look at.
If he was actually Baptist when he was born, and the birthdate is correct, this suggests the possibility of southern US Loyalist family. There weren't any other Baptists in NB at that time. The New England Planters were largely Congregationalist and Presbyterian, and the Baptist faith came to the northern colonies along with the Loyalists in 1783/4. But I might keep an open mind, because a lot of my ancestors converted to the Baptist faith in the decades that followed.
Happy New Year! I hope 2020 is the year you connect these ancestors.
