It appears that Martha's parents may have been James Whelpley and Eleanor (no last name). He was born in 1793 and she in 1813. Their children: Margaret, b. 1839, Charlotte, b. 1841, Frances (Fanny) M., b. 1843, Amelia b. 1850 and Martha, b. 1853. All were from Kingston, New Brunswick. They are found in the 1851 and 1861 censuses of New Brunswick. James is missing in the 1871 census. Eleanor isn't found either but may have remarried.
James would probably have been a son of one of the oldest four sons of Darling Whelpley, a loyalist who arrived in New Brunswick in 1783.