UK reisdent Zimbabwean passport holder wanting to visit Australia

Hi
My wife is a Zimbabwean passport holder resident in the UK. She is about to get ILR and wants to visit family in Australia for 3 weeks. Difficult to find easy answers to these questions so appreciate some help:
1) Can she visit Australia considering she has ILR in the UK but is still a Zimbabwean national?
2) How long on average to get the visa (she wants to travel in the next 2 weeks)
3) How/where do we apply?]
Thanks