Ok, thanks everyone.
Once again, as there seems to be some misunderstandings:

First we are landing in
Sydney and have 5 days there.
So where would you legally and safe kite there? As I said we were considering storing our quiver at the airport. Were not planning on renting a car either.

Then we are flying from Sydney to
Byron Bay, and have 5 days there. We will rent car at the airport so we will be mobile.
If there are any beaches to legally kite and any that are banned we would like to know.

Next is trip in the campervan from
Brisbane to
Cairns over 17 days
(starting on 22nd March, so we are hitting high season around Easter holiday)
Kite Quiver:
We got rid of our big kites, we don't bother going out if our 9 meters aren't enough.
Saying that we both are on a light side and usually take smaller kites than most people.
Ireland being a windy and stormy country we also have 6m each. So we thought about bringing our 9m x 2 and wondering whether take 6 at all, or maybe just one...
Thanks for all the help and info.
P.S. Yeah, we plan to spend about 2 days with full day drive so we can get more rest time in cool places. We are not interested in stopping st every tourist attraction.