Hehe the creepy-crawly question
The big scary spiders are pretty harmless (not that that makes them any easier to deal with hehe!), the only spider you really have to worry about in brisbane is the redback. They're pretty small - just keep your outdoor furniture free from webs and maybe check underneath things that've been sitting around outside or in the garage before you stick your hand there. The only snakes I see in the city are little white-belly snakes and green tree snakes, both of which are fairly harmless. I found a little white-belly snake in my covered sandpit when I was little but there aren't as many around now.
I've never had a problem with a spider or snake bite, nor has anyone I know. It really doesn't happen because most people use common sense and it's so rare to see one that's actually dangerous anyway!
OT: I always wonder... do they not have snakes and spiders over there where you live? People from the US always ask about it... it's funny!
As far as renting with pets, it's up to the landlord. Usually the realestate online listing will say No Pets or Pets OK - obviously with a big dog the fencing is important. Real estate agents are usually pretty good about replying to emails and their address will be the contact on the listing, so if it's not mentioned then definitely ask!
I live in a "No Pets" and secretly have a cat, I'm not worried because you get two weeks notice on inspections etc. But a big dog is a little harder to hide
Buying organic in Bris is really only affordable if you go to a market. Quite a few new ones are starting up around the place. I get all my fruit and veg direct from the farmer, if not organic. We manage to feed 5 adults on about $90 of produce a week, and we eat quite a lot of veggies. It's only that cheap because we drive to the markets and buy bulk.
I think that income sounds like you'll be quite comfortable... but this is coming from someone who is technically below the poverty line