no problems !
There should be no problems with what you plan , by UK standards the airspace is empty of traffic and the control zones are far apart so expect low stress flying.
You will be flying over some rurul areas that may seem to you to be empty but by australian standards it is highly populated , on all the flight plans you have to nominate a "SAR time " this is a time when if your flight plan has not been closed the search and rescue system starts to look for you.
These times are all in UTC and so with local time being 12 hours displaced from this some care must be taken not to give a SAR time that is wrong.
The australians expect a high standard of pilotage and have had some problems with american PPL holders getting in to trouble and so the check flight you will have to do will be a full australian bi-annual flight reveiw , this should be no problem for a UK PPL holder and will be a good intro to flying in australia.
You will undoubtedly have a lot of fun but remember to do all the pre-flight planning well because of the distances involved.