brisbane to 大堡礁

From Brisbane to Great Barrier Reef (Cains) is long way by road. It you have time or want to drive, it take ~10-12 hours to drive up but the view is great along the coast.
However, you may take a plane from Brisbane to GBR which take ~2 hour for a few hundred $A then you can take a local tour. I would advise you not to join tour from Brisbane because more expensive. A local tour from Caine ranges from ~$A200 for a day tour to >$1000 for a 2-5 days expensive tour. But there are lots informationsat the airport or in the Hotel.

Enjoy the trip and holiday.

Depends on which part of great barrier reef you are going to, for it is huge.
Refer to
http://www.barrierreefaustralia.com/the-great-barrier-reef/reefmap.htm
http://www.arta.com.au/qldmaps/gbr.html
Most tourist goes to Cairns or Whitsunday, you better take a plane to, or check the local travel agent.

You are in Brisbane, you are so close to 大堡礁. Because 大堡礁 is along the coast, if you have driving licence you can drive there by yourself. If not, you better join a local tour. Price is base on how many days you stay in 大堡礁.