Do you have something definitive showing your Major Phillips had a daughter Alice? I only as because of the wording in the original post, "may of had a daughter..."
I tried switching it up for a John Pearl. I came across one the approximate age to match what Alice would be, but he is married however to a different woman,
John Pearl b: c 1775 NS
d: Oct 1844, Billtown, Kings, Nova Scotia
married to Susanna Chappell.
If you have any other information, I can keep looking for you