The most common and most likely answer to this crossword clue is the 6 letter word SPOUTS
I've seen this crossword clue in The Guardian
S
P
O
U
T
S
More clues leading to the result SPOUTS
Buddy explains!

The straight part
We know that "Rabbits" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rabbits = spouts.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SPOUTS mean?
SPOUTS noun- A tube or lip through which liquid or steam is poured or discharged.
- A stream of liquid.
- The mixture of air and water thrown up from the blowhole of a whale.