Wally,
I use CGU and NRMA but there are others.
Shop around because prices vary depending on your property's location and your individual needs & circumstances.
Don't worry, all landlords insurances will cover you for the duration of the tenancy.
Read your rental agreement
EXPIRATION OF LEASE
Should Tenant remain in possession of the premises with the consent of Landlord after the natural expiration of this lease, a new tenancy from week to week shall be created between Landlord and Tenant which shall be subject to all the terms and conditions hereof.
So after the main lease expires you still have a weekly lease and you are still covered
Cheers