Not for quids is similar to not for love nor/or money:
if you say that you cannot or will not do something for love nor money, you mean that it is impossible to do or that you will not do it whatever happens It's incredibly popular. You can't get tickets for love nor money. He's hopeless and unreliable. I wouldn't give him a job for love nor money.
The Concise New Partridge Dictionary of Slang and Uncoventional English (2008) says:
Quids noun a large amount of money AUSTRALIA, 1930 • not for quids not for anything AUSTRALIA, 1947
This is from the monetary quid, which was the Australian pound (fixed in value to the pound sterling) at that time, and not sovereigns or guineas.
I found a 27 January 1947 example in The Sydney Morning Herald, an instalment from Esther Roland's novel I Camp Here:
"I'll swap you jobs," Garth said, hitching at his trousers.
"Not for quids," grinned Jack. "I don't like the way the snorty ones fizz down your neck as you sit there."
I found an earlier example from 1921 in Beauty and Nick by Philip Gibbs (read online; first published 1914):
"Can you give me her private address?" asked
"Not for quids," said the man. "It's as much as
my job is worth to give any lady's private address."