Some brief notes:
There is a dedicated "H1ag and Subclades Project" at Family Tree DNA. The map for that project, when set to display H1ag1, shows a strong localization for Most Distant Maternal Ancestor among its members: Scandinavia and UK. That suggests a Scandinavian origin for the H1ag1 haplogroup's founder. The article on mt-haplogroup H at Eupedia suggests a northern Europe origin, though with no source/citation given.
The predicted founding age of the parent haplogroup, H1ag, was estimated as roughly 4,300 years ago in the Behar et al. 2013 published paper (as displayed here), so the founding of H1ag1 would be after that. The H1ag1 haplogroup was recognized after the Behar paper was published, so there's no calculation for it there.
The DNA of an ancient H1ag1 haplogroup member (designated "HI2") was recovered and characterized in a 2016 scientific paper (also as a preprint). He lived during the late Iron Age (around 100 BCE) and was buried in Hixton, England.