Budgie is a shortened form of Budgerigar, from the native Australian name Betcherrygah. The betcherry bit means ‘good’, and gah means ‘parakeet’. There is some disagreement over the precise nuance of the ‘good’ part – it may mean ‘good to look at/handsome’; it may be ‘good’ because a flock of budgies indicates a good water supply (a useful guide for native Australians); or it may refer to the birds’ potential as a snack. It was certainly on the menu of the aboriginal people of Australia.

The surprising meaning of the word budgerigar
The slight confusion over the meaning of ‘budgerigar’ is increased further by the theory that the native word betcherrygah is onomatopoeic - i.e. it imitates the bird’s twittering voice.
The word 'budgery' (without the ‘gar’), sometimes written as 'boojery', is an obsolete Australian English slang word, used in the same way as those largely meaningless but positive exclamations ‘Great!’, ‘Excellent!’ or ‘Awesome!’
, 18 January 2019
It is informative page I see indeed