A word that means "the yield of a hunt"

Solution 1:

Right in your first sentence...

catch noun: an act of catching something, typically a ball [or animal]. an amount of fish caught.

"a record catch of 6.9 billion pounds of fish"

"he inspected the catch"

and another for good measure...

quarry noun: an animal pursued by a hunter, hound, predatory mammal, or bird of prey.

"he would not allow his quarry to elude him"

google definition

Solution 2:

I would recommend "Spoils" or perhaps "Prize". They imply a challenge, competition or battle from which the caught rabbit is the "reward" - the hunt could be thought of as such in a metaphorical sense.

Spoils Merriam-Webster

1c : something valuable or desirable gained through special effort or opportunism or in return for a favor —usually used in plural**

3: an object of plundering : PREY

For example, you may refer to the caught rabbit as the "spoils of the hunt"

Prize Merriam-Webster

1 : something taken by force, stratagem, or threat especially : property lawfully captured at sea in time of war

2 : an act of capturing or taking especially : the wartime capture of a ship and its cargo at sea

Solution 3:

kill
noun [usually in singular]
an act of killing, especially of one animal by another: a lion has made a kill.

• an animal or animals killed, either by a hunter or by another animal: the vulture is able to survey the land and locate a fresh kill.

New Oxford American Dictionary

Solution 4:

Your question:

A word that means “the yield of a hunt?”

bounty: Cambridge Dictionary

f. [ C/U ] a large amount of something [ C ]

As in:

The hunt resulted in a bounty of game.

and

I was amazed by the bounty of our hunt.

synonyms of bounty: abundance, plenty, exuberance, profusion, affluence, plenitude, copiousness, plenteousness

Solution 5:

bag

Noun

a quantity of game taken

(Merriam-Webster)

Related to bag (verb), the act of shooting or catching game.

This might be more British English.