Are you an Australian citizen? If so you will be able to claim benefits straight away, unless they decide you have moved from an area with plentiful jobs to one without in which case I think they can make you wait 3 months.

For your husband it depends how long he has resided in Australia as a permanent resident. There is a 2 year waiting list for benefits such as jobseeker payment but if he has already been here for that long and just moved away temporarily then he might get them straight away.