Are you looking for Brisbane Airport Car Hire? All the international companies are there and a great bunch of local ones too.
First thing to remember, if you're arriving from North America or continental Europe, is Australia drives on the left see photo below.
It's not quaint, cute or wrong, it's just different. Driving in Brisbane, unlike many other big cities, is pretty good despite what Brisbanites will tell you.
While it's true there are over a million people, and a lot of construction, it rarely makes a big impact on the traffic conditions except for the occasional detour.
And once you're out of the city the roads are practically empty, by European standards anyhow. The only time driving can be a bit of a pain is at rush hour, which is approx 7am to 9am and 4pm to 6pm. Even then it's not horrendous, except on a Friday when everyone is heading to the beach! Parking in the city is where the real pain begins.
It's generally limited and can cost an arm and a leg, which is why it's usually better to take public transport into the city. Car hire companies that operate at Brisbane airport include Avis, Thrifty, Budget, Europcar, Hertz, and Redspot Car Rentals.
Driving in the suburbs can be confusing and every resident of Brisbane has a Refidex or book of maps. Personally, I use a garmin, and that generally gets me to where I want to go with ease. Some people suggest that if you are going to be there for any amount of time to buy a street directory. This will help to help navigate the winding, turning streets that seem laid out at the whim of the designer.
This aspect of the city is very European, rather than New World. One reason for this is likely because Brisbane is full of hills, so if you've rented a manual car, make sure you get used to hill starts early!
The photo above is from Lamington National Park. I put it here to show driving on the left for those not familiar with it. Most people get the hang of it pretty quickly.
The usual comment is 'it's hard to get used to all the space on the driver's right' rather than the lack of space on the car's left.
If you decide that you want to fly into the Gold Coast International airport, often called Coolangatta airport as that's where it's located, you might find it less complicated.
If you are flying straight into this airport, you'll find the driving even easier because there's much less traffic and not so many hills.
Coolangatta also has car hire and other transport links for Brisbane and the Gold Coast.