I agree with the others that 2 acres of grass won't last long, Especially this time of year.
You might have better luck in the spring when the grass is growing fast and it might be able to keep up with the grazing.
As far as goats and grass go, Grass is the last thing that every goat I've had on the place will eat. They've really preferred brushy stuff, Which is great since that's the only reason I tolerate the fence ridin' bastids anyway.
I'm goat free right now and don't expect to ever suffer another one to set hoof here no matter what the wife and grand kids say.
