I plan to purchase a throw away cell phone upon arrival in Australia and understand Testa is the 'best' provider; but after Australia we will be going to New Zealand; do any of the providers in Australia also cover New Zealand?

Telstra has the best network in remote areas outside of the towns and cities in Australia but they are more expensive than the other operators

You can use a Australian PrePaid SIM in NZ but you will be paying roaming costs for both incoming and outgoing calls

Some of the other operators to look at and their roaming costs
Optus
Virgin
Vodafone
Lebara
Amaysim

I agree Telstra will give you the greatest coverage. They will cover NZ but not at the same price as they do within Australia. You might want to get a SIM card when you go there. They are not that expensive.

I lived in Australia for 6 months and honestly, I liked Optus so much better! You didn't have to deal with buying credit, and I had good service. But if you are only there a short time then Telstra is your best bet.

There's a great new provider offfering global contracts. One sim for every country - been a godsend for me as I'm forever having to change out sim cards and use different numbers to avoid roaming charges.

http://www.vendome.com.au/luxurymobilephoneservice/