Re: Who's your Moore
Most of the following is from the Rev War Pension abstractW16049 for James Moore of Pembroke, NH who m Abigail Noyes. This is available at NH Historical Soc Library and Washington Archives.
In 1804, James and Abigail moved to Canada with some of their children (John emigrated to Maine and Hannah, married, remained in Bow NH. Three of the male children(Isaac, Ephraim and Rodney) returned to the United States abt 1812 for the war leaving, I believe, sons Archibald b 1785, Thomas b 1787, James Jr b 1791, Washington b 1793 and Jacob Green b 1796 still in Canada. The ages of the men therefore would be respectively 30, 28, 24, 22, and 19 years at the time of the birth of your ancestor Mary "Dolly" Moore.
I suggest you, at least for a time, focus your search on the above men as possibilities.
Post if you need additional info.