Fallow like to tear holes in fences
Yes they do, if other fallow are anywhere near, you need to have double fence at 4'.
That said, deer and sheep specie are all bad for small $ making projects. Think about animals where both male and female are trophies. As in the oryx species. Scimitar are virtually bulletproof. You won't ever lose one to a predator, they aren't disease prone, and produce well.
But, if you choose scimitar you are gonna have big feed bills because you are so small. Don is right, you need more acres.