As a connoisseur of all things toast and by extension toasty, I believe I have the answer.
Urban Dictionary cites the phrase as;
toast my goats
1. If something amazing or outstanding happens this phrase can be used [as an exclamation] Well just toast my goats that was an outstanding throw!
2.if you are mad it can be used in the place of [other throwaway insults] Well you can just toast my goats because im out of here!
This phrase should not be confused with 'totes ma goats', which Urban Dictionary defines as;
Totes Ma Goats
slang for totally, used between full grown men in a bro-mantic relationship, to convey their excitement to a suggestion. Made popular by Paul Rudd's character in I Love You, Man. Sydney: Dude, we should rock out sometime. Peter: Totally.... totes my goats.
Guy 1: let's go downtown and [see if we can talk to women] Guy 2: Totes my goats!
However, I believe that it has deeper meanings, and via a long line of interpreted and assumed links that would be too time-consuming to list in its entirety here, I believe it holds the key to understanding life, the universe, and everything.
Dreams sprout tall so beautiful to wither and fall off Old and dusty, creaky and rough This clockwork will not rest