Is there a service that finds property for people that are looking to
rent in Brisbane?

Dear Ockie, 

The site Brisbane City Life writes "Most rentals in Brisbane are
private properties let through estate agents or direct by the owner.
Leases tend to be for 6 months. If you are moving to Brisbane, it is
difficult to arrange a rental property before you arrive here and you
may need to arrange some temporary accommodation in hotels, B&B or
backpackers hostels." (SOURCE: Brisbane City Life,
<http://www.brisbanecitylife.com.au/bcl/realestate/default.htm>)

Brisbane City Life offers the following guide to rental in Brisbane: 
Renting flats, apartments and houses in Brisbane 
<http://www.brisbanecitylife.com.au/bcl/realestate/rent.htm> 

Another good place to get tips on rental in Brisbane and how to rent
(or how to find a rental) is :
Our Brisbane - Renting 
<http://www.ourbrisbane.com/living/realestate/renting/> 0 the site
also includes listing of available property.

Here are several: 

Real Estate.com.au
<http://www.realestate.com.au/cgi-bin/rsearch?a=s&cu=&s=qld&ss=&ag=&t=ren&snf=rbs&tb=+BRISBANE%2C+&u=BRISBANE&is=1&pm=&px=&pme=any&pxe=any&minbed=&cat=&p=10&o=def>
(If this querry doesn't work for you, try:
<http://www.realestate.com.au/>, choose "rental" on the top bar, and
then choose "Queensland" and you'll have a direct link to real-estate
rentals in Brisbane.

First National Real Estate
http://www.firstnational.com.au/ - choose "rent" from the top bar and
then your region - you can get either agents, who'd find a suitable
property for you, or go dierctly to properties to let.

South East Queensland Rental Accommodation
<http://www.seqrents.com.au/> offers rentals in Brisbane and S.E. Queensland. 

A list of real estate agents and properties is available here: 
About-Australia
<http://www.about-australia.com/queensland/queensland-business.php?listtown=142&liststate=38&c=355&cat_id=63&LogoID=>

I hope this answers your question. Please contact me if you need any
further clarification on this answer, before you rate it. My search
terms were [real estate rental agency brisbane]

I have recently moved to Brisbane and found a real estate business
that will find rental property/s for people for a fee.  They do all
the inspections for you based on your requirements and will give you a
report including photographs and put you in touch with the real estate
agent that is renting the property.  They are called Property Hunters.
 Web site is www.propertyhunters.biz.