rabbit-catching net
A net specifically used for catching rabbits. The term is straightforward and literal.
猟師は兎網を仕掛けてウサギを捕まえた。
The hunter set a rabbit net and caught a rabbit.
Compound of 兎 (usagi, 'rabbit') and 網 (ami, 'net'). The reading うさぎあみ is straightforward.