edit: That was what was using your data, downloading WhatsApp. You can buy more credit now, it should be fine, just dont download or use the internet. No, you won't need a new phone :p
Yes prepaid is a good option. You're able to top up whenever you want and you're not locked into a cap. If you sign up for postpaid, chances are you'll exceed your limits, not just you, but many people do and thats how these phone providers make a lot of their profit, since they charge users at premium rates once they've used up their credit. Lets not get into that, but I think you should definitely stick to prepaid as you're in control.
However, if you're comfortable, switch to the Crew Cap where you get $200 credit and 100MB which costs $30 for 60 days or switch to Woolworths Mobile where you get $500 credit and 5GB (5000MB) of data which costs $26.10 for 45 days (with an everyday card). I was hesitant switching to Woolworths Mobile though, didn't want to pay $17/mo >.<.