Call centres. Yes, you can get set up to work from home. You have to be dedicated to the work, I.e. you can't nip off to look after the baby. It would have to be when DH was home or you would need to put the bub in care.
If you phone Origin Energy, you will find a number of their call centre staff are in their own homes. I chatted to one of them once.

Yes iinet do it too - you have to do a while (a couple of months I think is with iinet) in the office first though - and the shift patterns weren't that great to always have someone else at home in my opinion - but they are recruiting at the moment in Melbourne anyway.