A pay-monthly line will remain open for as long as your monthly bills remain paid - whether you use the phone or not, is immaterial. Equally, not maintaining your contractual payments will cause impacts to your credit file.
Migrations to PAYG cannot be completed abroad, your phone will lose network access once the SIM is moved to PAYG - and this can only be resolved by registering it on EE's UK network. Thus you'd need to give cancellation notice at least 31days before travelling, to allow time for your new PAYG SIM to be used in the UK first - completing activation & enabling roaming.
Inclusive roaming is subject to the Stable Links Policy which broadly requires usage in the UK for 2months in every 4. You could potentially purchase £25/weekly roaming passes to allow inclusive calls, texts & mobile data in the short term : Then once you have a more permanent local arrangements, just maintain your contractual payments and pay for calls & texts on a per-minute/per-text basis, forgoing roaming data.
Alternatively, migrate to PAYG & then pay the prevailing roaming rates for PAYG roaming in Australia - just being subject to the hibernation policy to prevent the line being suspended.
