My husband and I live in Brisbane, and I work in Redcliffe. $2000 per week sounds like heaps. Brissy is not that expensive. You will be able to get a nice meal in a cafe for less than $20AU each. We normally don't pay more than $16AU. China Town in Fortitude Valley, easily reach by train or walk from the city, has great restaurants, pubs, asian food that won't break the bank. Most restaurants are BYO, so pick up a bottle of wine before you go, will save a lot. Liquor shop has wine for less than $15, restaurant will charge about $40. The restaurant will charge corkage, normally about $2 per person, some places just $3 per bottle.
Public transport in Brisbane isn't great, but rent a car and travel possibilities become endless. There are some cheap rental car places around. The one I can think of off the top of my head is Able Car Rental. I think they have cars from about $30 per day. Just have a look at our Yellow Pages on-line www.yellowpages.com.au and search through the different rental companies.
With a car, you can easily go up to the Sunshine Coast, about 1 hours drive from Brisbane. Well worth the trip, and the place all the locals go, as the Gold Coast is very touristy. If you just want to relax on a beautiful beach for the day, the Sunshine Coast is the place to go.
I wouldn't stress about the wildlife. Let your husband know, most of our spiders are harmless, even the ones with a bad name aren't that bad. We live here, and hardly ever see a redback spider - probably the most common venomous spider in this area. While they are dangerous if they bite small children, I don't believe an adult has died from a bite in a very long time. You won't need to be checking the bed every night before you get in or anything. It is really not that bad. Your chances of running across a snake are about 0.1%. Even living here, I would only see maybe one a year if lucky, and then most times they are just tree snakes which are harmless. If you do see one, which I doubt as you will not really be off the beaten track, you just need to use common sense, don't annoy them, they won't annoy you.
Have been horseriding in Byron Bay once. Can't think of the name of the company, but they do horseriding on the beach, and you get to go into the waves with the horses, and they surf the wave back in. Great fun!
Remember to bring, sunscreen (vital or you will ruin your trip with sunburn, nothing worse than blisters on your butt), insect repelent (mossies are a bit annoying over here around dusk, depending where you are, so you don't want to be scratching all the time), a hat, and drink plenty of water. If you think 19 degrees is warm, its about 30 today and overcast (which is unusal for Brisbane, normally blue sky all day every day), so you are really going to feel the heat.
Hope this info helps.