If Sean is correct about the ending -tator, the name might mean "Daughter of a Doxie".
Doxies are sprites that look like Pixies. I think in some Celtic stories, they are horse-like in shape and can change shape into strange humans with horse-ears, but I may be confusing them with Nixies or Kelpies.
On the other hand, the name could be from the same root as the Old English word "Dohter", meaning daughter. Often times surnames pick up strange elaborations over the years, so it can be hard to tell.