Yes, they do have a clinic, I didn't actually use it as they are 20 mins away from me and so I just went to the QH clinic round the corner from me. A friend of mine had her first baby at GC Hosp and did not BF due to no support, she had her second at JF and had excellent support while there and is stil BF 5 months down the track with no plans of stopping anytime soon.
I BF for 7 months, they definately encourage it and minimal intervention on the birth side of things which I really liked.