Birds in Backyards have some info here if you're looking for more.
They say these birds are easily recognisable because of their red rump, eyebrow and beak. So, I might remember what they are next time I see them!!
The brilliant red is what caught my eye. They're tiny birds, and so unless you see the red, they could flit right past me. They're a bit like the male Superb Wrens with their dash of blue - the brown females fly all around without me getting excited, but once that dash of blue appears, out comes the camera!
The red-browed firetails do shared parenting duties of nest building, incubating eggs, and rearing chicks.
My trusty Pizzey book tells me that these belong to the family of Grass-finches. Grass finches are very social in non-breeding season and form large groups, but it appears that they have strong pairings during mating, which may last a lifetime.
It makes me wonder how people know if birds mate for life or not. Did they observe bird pairs and were they able to identify each individual? Were they tagged? Hmm...that's a lot of research to conduct!