I worked for an Australian company from Germany and did similarly (I worked German work days but would start early ~5:30-6am to have some overlap with the Australians - they never expected me to work "core hours", just to have some overlap).
It wasn't too bad! Much easier than working with west coast US (where their 9am is my 6pm - I don't want to work late but I don't mind working early).
9am in Pacific time is probably more like your 3-4am (depends on where in Aus you live) - certainly you could create 'core hours' 1-5pm Pacific time which would at worse be your morning (early morning in your winter)
It wasn't too bad! Much easier than working with west coast US (where their 9am is my 6pm - I don't want to work late but I don't mind working early).