There's a rhyme that's similar to this one called 1, 2, 3, 4, 5, I Caught a Hare Alive.

Notes

I found the following variation of this rhyme in A History of Nursery Rhymes by Percy B. Green (1899). He called it "a game for a wet day". Green's comments and instructions on how to play it are in italics below...

Cows and Horses Walk on Four Legs

Cows and horses walk on four legs,
Little children walk on two legs;
Fishes swim in water clear,
Birds fly up into the air.
One, two, three, four, five,
Catching fishes all alive.
Why did you let them go?
Because they bit my finger so.
Which finger did they bite?
This little finger on the right."

The enthusiasm with which children of all ages play this somewhat noisy game can hardly be imagined. Try it, you fun-loving parents, and be rewarded by the tears of joy their mirth and laughter will cause.

It is played after this fashion. However, it will not be amiss to remove the tea-things before anything is attempted. All seated, the parent or nurse then places the first and second fingers of each hand on the coverlet [note: coverlet = tablecloth], the youngsters imitating her. Everybody's fingers are now moved up and down in a perpendicular way, like the needle of a sewing machine. All singing -

"Cows and horses walk on four legs."

The next line requires a change, only one finger on each hand being used, and -

"Little children walk on two legs" (sung).
"Fishes swim in water clear"

demands the waving of arms horizontally, to imitate the action of swimming in water.

"Birds fly up into the air."

When this line is sung the hands are held up, and moved from the wrists like the wings of birds flapping in the air.

"One, two, three, four, five"

is said to the clapping of hands.

"Catching fishes all alive"

is sung to the action of grabbing at supposed fishes with the fingers.

"Why did you let them go?"

Everybody shakes their head and replies -

"Because they bit my finger so!"
"Which finger did they bite?"

Holding up the little finger, you answer -

"This little finger on the right!"

*****

Here's the version of this rhyme from The Little Mother Goose (1912), illustrated by Jessie Willcox Smith:

One, two, three, four, five,
Catching fishes all alive.
Why did you let them go?
Because they bit my finger so.
Which finger did they bite?
The little finger on the right.