on one hand, I definitely want this, on the other, I can see how "OP" this is and this revert back to don't have a reason to leave the base.
What I think is make it a skill and how much animal you kept is base on the skill. And there need to be something offset it a bit so it not just free resource.
My version of this suggestion.
Level 1: chicken/rabit cage schematic to put the animals in (also help not rendering the animals and take away game resources), 4 animals per cage (2x1x2). hand net schematic (to capture/move them).
Max animal capture is 2, if you tries to put more in a cage, it will say "X escape you when you try to put it in the cage".
Chicken can produce egg and feather with only one present. with 2 it also produce meat.
Rabit need 2 minimum to produce meat and leather.
must feed animals vegetables or seed (treat like fuel), once food run out, animals stop giving resources. produce items once every day, amount given is the same as killing 1, amount of egg is the same as bird nest.
level 2: max animal is 4.
level 3:max animal is 6.
level 4: max animal is 8.