Fairywrens (Maluridae) are restricted to Australia and New Guinea. Despite the name, they are not related to Northern Hemisphere wrens (Troglodytidae). It's another of those cases where appearances are deceptive.
If this species doesn't ring any bells, you might be familiar with its relatives, the superb fairywren (M. cyaneus) of SE Australia and splendid fairywren (M. splendens) of Western and central Australia. There is certainly truth in advertising when it comes to common names in this group. The superb fairywren is superb, the splendid fairywren is truly splendid and this one does, in fact, have a red back. (Although some of them are more orange, but we'll ignore that. *Makes hand gesture* These are not the fairywrens you were looking for.)
The red-backed fairywren occurs in NE and N Australia, where it lives in tall grass and scrub. I used to see them frequently in the cleared areas near the rainforest, but never managed to get a really good look at them. They are much more obliging here.