This is a too simplistic analogy of economy. The source of "money" is not people, it's trade (read "On Money" by David Hume (1752)), which always happened between people, but not only anymore. Examples of this: trade bots, smart contracts (which are just programs managing money).
The problem with this analogy is that we're not replacing rabbits, we're working very hard on developing nutritious artificial grass, created directly from silicon.
You don't need humans making transactions for things to run, you just need entities capable of decision making.
We are talking about a world here where humans are entirely out of supply chain. Rocks in your analogy rather than grass or rabbits.