I live in North Queensland, I can promise you that while Telstra certainly does have the best coverage it is not perfect and there are spots up here where you won't get Telstra. In fact I've even been places in Tasmania without Telstra coverage, though that was about 8 years ago.
Of course minesites would have Telstra towers, that's no surprise.
OP, I would suggest Telstra or someone who resells Telstra, such as Boost (cheaper than Telstra but uses their network) provided your phone is unlocked and you can swap out the sim card.