Decide whether to break Australian tax residence
Just leaving Australia doesn't make you non-resident for ATO purposes — the resides test, domicile test, 183-day, and Commonwealth superannuation tests still apply. The cleanest break is to genuinely cease habitual residence (no Australian home, family relocated, intention not to return), notify the ATO via your tax return, and obtain a Certificate of Australian Residency for any year you're claiming dual coverage. If you keep Australian residence by accident, you'll be taxed by both countries on global income (with DTA relief).