The Tooth Fairy is listed on the excellent Pride of the West album by John Wynne and John McEvoy (track 9 - Edward On Lough Erne's Shore/The Tooth Fairy/Fraher's Jig)
but it isn't the same tune as this...
https://www.youtube.com/watch?v=Rm_FyS7ceSc which is also called the Tooth Fairy and composed by André Brunet.
So does anyone know the correct name of the tune on the Pride of the West album
edited - just found this info with a sample of the tune https://www.irishtune.info/tune/4884/
Seems that there's more than one Tooth Fairy, The / An tSióg Fiacla (composed by Orla McAtavie) ! Great tune IMHO.