Notes:

I cannot prove that Mary Whitney was the daughter who died in 1719; however, in 1718 the only children living were Josiah, Jonathan, Abigail, and Mary. All of the other children have records after 1719 and I find no other records for Mary.

Birth:
"Massachusetts, Town Clerk, Vital and Town Records, 1626-2001," database with images, FamilySearch (https://familysearch.org/ark:/61903/3:1:3QS7-L979-WQCB?cc=2061550&wc=Q4D4-16D%3A353350501%2C353606501%2C353612601 : 13 July 2016), Norfolk > Wrentham > Births, marriages, deaths 1681-1807 > image 28 of 506; town clerk offices, Massachusetts.

p. 45
Whitting
Mary Whitting, the daughter of Josiah Whitting and Mary his wife, was born March 5. 1695/6
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Orestes T. Doe, ed., The Record of Births, Marriages and Deaths in the Town of Franklin from 1778 to 1872 (Franklin, MA: The Franklin Sentinel, 1898).

Died:
Ancestry.com. Massachusetts, Town and Vital Records, 1620-1988, Wrentham Deaths, p. 514

Whitney, [torn], d. of Josiah and Mary, Apr. 24, 1719.
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"Massachusetts, Town Clerk, Vital and Town Records, 1626-2001," database with images, FamilySearch (https://familysearch.org/ark:/61903/3:1:3QS7-8979-9D3K?cc=2061550&wc=Q4DW-7M3%3A353350501%2C353606501%2C353607001 : 20 May 2014), Norfolk > Wrentham > Births, marriages, deaths 1668-1913 > image 159 of 748; town clerk offices, Massachusetts.

[torn] Whitney ye Daughtor of Josiah & Mary his Wife Died April ye 24 1719.