Sort of yes and sort of no.
First read this:
http://www.dpi.nsw.gov.au/hunting/rules ... ting-guideSecond, to quote the website: You are not required to hold a NSW game hunting licence if you are: hunting rabbits, foxes, feral goats, feral pigs, hares, feral cats or wild dogs (other than dingo) on private land.
You need an R licence for deer on private property that you don't own. Technically, you need it for deer even if you do own the land, but because of the damage deer cause they've put the regulations on suspension.
You don't need a letter, but you do need at least verbal permission. And its a good idea to get a letter anyway because it heads off trouble before it starts, if anyone questions you.
As to minimum size, not as far as I know, but there is probably a practical limit before it's unsafe, depending on what exactly you're doing.