Hi Helen
My Son has shipped his two staffies out (seperately) with :
www.airpets.co.uk who are based at Heathrow they are specialists who do it all the time and really do know the ropes.
Have a look at their website and then ring for price and information pack
It's costly to send pets but very important to get paperwork and bloodtests done correctley - and in the correct time span.
Just be aware that you need a UK vet who has experience or will look up requirements - for example, the normal UK vaccinations include a Leptospirosis vaccination which will show up in bloodtest for some 6 months and is not acceptable to Australia.
Airpets do it all the time and arrange for quarantine in Australia (I believe there are still only 3 - Sydney/Melbourne & Adelaide I think)- for one month - they are looked after and you can visit (probably stressful for the dog) and also speak to the carer for re-assurance.
Good luck to you and staffy
Hugh