I'm in the U.S., so I don't know how it works in Australia. Generally in the U.S. if you wish to donate a kidney and do not have a particular recipient in mind it is the hospital or donation program that selects your recipient. Through
www.kidneyregistry.org they would try to match you with a recipient who has a willing but non-compatible donor. You donate to that patient, and then that patient's incompatible donor donates to someone else chosen by the program. Again that "someone else" is another patient with a willing but incompatible donor who passes along a kidney to the next patient. So the initial "non-directed" donor sets off a chain of many otherwise impossible transplants. I don't know if they have this sort of thing in Australia.
If a donor has nobody in particular in mind but wishes to choose their recipient they usually have to do this on their own. I believe there are facebook pages devoted to such matches. Also
www.matchingdonors.com (.org?) lets potential donors and recipients post there and find each other, but I believe they charge a fee. At
www.livingdonorsonline.org there is a "looking for" section where patient post there need for a kidney (no Fee for posting.)
I hope this information is helpful.
Fr. Pat
Since you are "B+" your blood type is compatible to donate a kidney to another "B+" or to a "B-" or to an "AB+" or to an "AB-". But individual tissue matching with the particular recipient is also required.