if it's in your own property, maybe. 最近我家附近几个小city为猎杀鹿这事闹得厉害,据我所知地方政府是有规定的。好象 用枪的要有licence,用弓箭的没有。insurance is optional for both. don't know about ducks.
If you hit a deer and the deer died, I remember call some organization or police to report it, if they are okay then you can take the deer home even without a license.