>>1434312There are two types of permits that you can get for shooting them in Tasmania; a game licence or a crop protection permit.
With a game licence you can shoot as many as you like provided you do not use a spotlight. Common methods include using dogs to flush them out of the bush and shoot them with shotguns (pic related), or shooting them at dawn and dusk with small calibre rifles.
With a crop protection permit you can use a spotlight. I grew up on a farm shooting wallabies off the back of a ute every weekend. We'd keep a few for dog meat and maybe one for home if it was a good one, the rest were left for the (Tasmanian) devils.
With either license you report your take to the department of primary industry at the end of the year for population modelling purposes.