I got her quest just after reaching 5 hearts with Anna and cured her depression. By how Frost's quest works, you definetly need 4 hearts, access to studio and having fucked Anna raw. That's, since the pills from Dr. Frost are used on these conditions.
The 1.8 update is sooo good. I like the Dr. Frost quest a lot. A shame that the body modifications are only treated as Studio toys. Devs, could you add an option to make these changes on Anna permanent? And maybe the option to give the pills to the other girls, just like the Lactation pill