No matter which context–home improvement, military, whatever.

(I’d never heard of the sexual context, but it is there, I discover just now.)

The Urban Dictionary has “getter”–but that’s weird to me. (it also has, apparently, “get ‘er done.” )

It’s so definitely a contraction, and the “her” choice of pronoun (instead of “it” and “him” ) I always thought came from the simply fact that it’s easier to pronounce than “get ‘im”, and there is no contraction for “it” and “get it” is kind of awkward.

Plus, the personification has a nice feel to it.

I’d have wanted to write it “get ‘er done.”

But here is how Larry The Cable Guy spells it:
Git-R-Done!
http://www.larrythecableguy.com/
and his fan-club site is: http://www.gitrdone.com/ (but hyphens on the site itself–I guess hyphens don’t work well in URLs? Or they decided not to confuse people by putting them in?)