"Old MacDougal Had a Farm" is known as a title in the States, but attached to the usual Old MacDonald Eee-1, eee-i. eee-i, o version. From University of Illinois Extension, Nutrition literature, credited to the "Youth Curriculum Sourcebook" of the Univ. Wisconsin Extension Staff, 1994.
It contains one verse seldom used in most sing-a-longs, and Old MacDougal becomes female, e. g.:

On that farm she had a fish
Eee-i, eee-i, eee-i, o.
With a blub blub here and a blub blub there,
Here a blub, there a blub,
Everywhere a blub blub,
Old MacDougal had a farm,
Eee-i, eee-i, o.

It concludes with-
On that farm she had lots of animals
Eee-i, eee-i, o, followed by another enumeration of all the animals and their sounds.

The following song is from a Flemish student website in Belgium:

Lyr. Add: Old Mac Doodle

Old Mac Doodle had a little farm
Down to the Ohio-io
And on his farm he had some pigs
Down to the Ohio-io
And a grow-grow here
And a grow-grow here
Here a grow
There a grow,
And ev'rywhere a grow.

Down by the stream (bis)
That's where I go (bis)
Back to my home (bis)
I dare not to go (bis)
For if I do (bis)
My rent I owe (bis)

Have you never seen a nigger
With a big eyebrow?
Down to the Ohio-io?

I have separated the text into three verses for clarity. More than one song seems to be combined here. Is the 'grow-grow" imitative of the pig's grunt? Notable mostly for the 'Ohio-io,' which appears in the 1917 version from "Tommy's Tunes."
Mac Doodle

Also this:

Lyr. Add: Cookie's Old MacDougal Song
'Just the chorus of a classic'

When Old MacDougal blow his bugle, me I, me I google!
With a google, google here, and a google, google there
Here a google, there a google, everywhere a google, google
When Old MacDougal blow his bugle, me I, me i google!

MacDougal Song