Hardly.
First off, The Oz government wanted nukes in the 60's-70's (neither the UK, or the US government trusted the Australian Counterespionage department (ASIO) to keep it safe... They had a reputation much like that of a Sieve... A popular joke in Australia's capital goes "How do you spot the ASIO agent? He's the one in the Dark suit, wearing an ASIO baseball cap standing next to a truck marked "ASIO").
They also have a heck of a lot of uranium to build em with, and a lot of Nowhere to test em in (which they were happy to let the British use).
Thats also not to forget Australia's defensive situation... A whole lot of land and a population to low to defend it alone - Australia always has, and would continue to need to, tie itself to a greater power - Originaly Britain, and since WW2, the US. A forward nuke base in Fallout's universe is possible
Even if it doesnt have nukes, its suppling the fuel for its friends.