LOLZ. OZ and Austrailia have several large US space tracking stations (For satelites, space missions, ect) Plus, if I recall from my days in the service, both nations serve as ports of call for many US military vessels.
Short version is: Both countries would have warheads paying them a visit.
(Forgive any spelling or grammar errors, got out of surgery yesterday and they have me taking Oxycodone for the pain.)
Assuming a similar treaty situation existed in the fallout world as in the real world, Australia would be compelled to join the war on the US side by way of the ANZUS treaty.
ANZUS was signed in 1951 (near the point of divergence), which increases the chance that it did exist at one point, if not at the point of war.
Until 1984 the treaty also would have compelled NZ to come to the defence of the US as well. As this change was definately "post Divergence", it could well mean that NZ would have been compelled to act too.
Australia, NZ and the US are also signatories to the UK-USA security agreement which gives us the ECHELON signals interception which is designed to intercept as many satelite transmitted communications as possible. Although Echelon dates from the 60's (Post divergence), it is an extention of previous treaties signed in the 40's, meaning in fallout's world Australia and New Zealand could have played a very important role in the US's intelligence gathering network, making them targets.