what was up with Charlie's accent?

Yes. The assumption can be made that he and his brothers were from Ireland and were outlaws. At the time of this movie Australia was just being 'civilized' (as Capt Stanley often says) but much of the population was made up prisoners from the United Kingdom who were deported for their crimes. Australia was essentially a prison for the UK then.

Exactly.
Of course, Guy Pearce is Australian, but his character, Charlie, was Irish.

*Correction: Australia during the 1880s was not still a "prison" - whilst the last convicts were sent to Australia in the 1860s, in most states it was as early the 1850s. By this period the majority of the population were either free born or composed of free settlers who migrated to Australia during the gold rushes or for agriculture.

Most of Australia was 'civilised' at this point - after all the British had been there for over 100 years. It was just the very outback areas that were lawless, like the Wild West in American during the 19th century.

But to answer the question, there were lots of Irish immigrants in Australia during the latter 19th century for the same reasons as there was in the USA - the potato famine. So it can be implied that the brothers were Irish immigrants.

I beg to differ that the Australian accent didn't necessarily evolve over a short amount of time within the first century the country was settled. Since it was mostly made up of immigrants and convict descendants from around the globe mostly from England and Ireland.

So whenever I hear an Aussie accent in a Colonial set drama like this I feel like its very out of place in time and context.

Have to say Guy Pearce was one of the few non Irish actors I’ve seen who successfully pulled off the Irish accent as well, he was brilliant.