"Mockingbirds" could be a non-Ozzie mishearing of "kookaburras" - which is how I learned it around 1965.

They had a "cheerful, laughing song."

The Oxford English Dictionary gives an example of "prairie" (in the obsolete variant "peraira") from Australian novelist Rolf Boldrewood's 1880's bushranger novel, "Robbery Under Arms."

However, the speaker is an American from Arizona.

But, in the song, if not "prairie" or "peraira," what would fit?