Hello,
Two companies that come to mind providing wireless service in Australia are Telstra and Vodafone:
https://www.vodafone.com.au
https://www.telstra.com.au/
Like most such providers they have contract and prepaid plans. Contract plans are usually more cost effective, but they obviously require signing a term contract, likely for 2 years. Both companies have prepaid plans for mobile broadband starting at around $30 for several gb of traffic. Of course, if your daughter can find a free WiFi hotspot she wouldn’t need to buy the prepaid card.
Regarding telephone calls from her mobile phone: she can either use her UK phone to place/receive calls in roaming (this isn’t usually an inexpensive method), or she can buy a local SIM card with an Australia mobile number. It would be cheaper if you called her using some prepaid service such as https://www.localphone.com or https://www.rebtel.com because you probably have access to free local calling while she doesn’t. The services mentioned above charge low rates to any country, but in order to connect you must dial a local number.
One other thing you should know is that calls to mobile phones cost more and most calling service providers advertise the low rates for calling to landlines. If your daughter called you on your cell the above might explain why she didn’t get all the promised minutes.