The extraordinary nanny meets the extraordinary Doctor! I've actually read a few fanfics that feature Mary Poppins as either a Time Lady or a human manifestation of the TARDIS. I think I might have also heard some headcanons that Ms. Frizzle is a Time Lady herself with her school bus being some kind of TARDIS.
This is so perfect I wonder how we haven't come across this before. (She's got the right idea with the purse Tardis. Way easier to carry around than a police box, though it's probably harder to enter. o3o)