Kankama said..I will brag here - I was a Laser NSW state champ, youth national champ and 20th in the open worlds in the Laser. You will die. I would not do it and I can gybe a Laser in 25-30 knots. I can square run a Laser in big winds - for a while. You cannot, almost no-one who doesn't train lots can. As for ten knots - again totally incorrect. A ten knot average means you are hitting 15 often and that is incredibly rare on a Laser. Here is a video of Mara Stransky sailing offshore. Mara is our women's Olympic rep. Her parents followed her in the family livaboard catamaran. She has sailed since she was born and is one of the best sailors I have ever seen. She capsizes and she is better then any of us. She gets absolutely exhausted by the trip.
Or this is Michael Blackburn - Laser Worlds champ - crossing Bass strait. He took a decade to learn to sail a laser really well.
Back to how to do it. I am a sea kayaker too. Paul Caffin, Freya Hoffmeister and Stuart Truman have all circumnavigated. I would not do it in a kayak. The best boat for me would be a small version of a Malibu outrigger - stable, fast and easy to right after capsize. Gary Dierking has a beautiful design called the Ulua which would be fab for a trip up the coast. Safe, fast under paddle and sail, light enough to move up the beach on your own. I would take a ply version of this boat.
Read Trumans book. Then go to a sea kayak convention and talk to people who do this type of stuff. Sail the east coast in the autumn in an Ulua. That would be fun.
Don't take a Laser.
I have been pick up boat for races at RQYS and seen Laser sailors after an hour of racing in 25 knots and only a metre of sea so exhausted they just can not rite their Laser for love nor money. As Kankama said you would need to be an elite Laser sailor and I would ever say they would struggle to keep going in the open ocean in 25 knots for more than a few hours. A Laser is not the sort of boat that you can just hove too in 25 knots and a 3 metre sea ( which could be a lot worse) and take a rest.
It is totally unrealistic to think you are going to average 10 knots in a Laser. My 57' yacht will blow the door off a laser and we generally look to cruise at about 8 knots average. I would think you should be looking at 5 to 6 knots average as you will be pulling the pin on sailing that day if the wind is over 20 knots and you will not always get that perfect sailing angle for speed ( 90deg apparent) and god help if you get it on the nose. If you look at the winds in Darwin you will see in can be very light winds for days on end at certain times of the year and also huge tidal flow.
But most of all I do a lot of fishing in the Northern Territory and the last place I would like to be is sitting on A Laser drifting slowly towards the bank with Crocodile swimming along behind me. There is not a day go past where we don't see a crocodile and that's not counting the ones we don't see. Sharks are also huge and thick up there, earlier this year our 4.9m boat was charged by a huge Hammer Head shark which scared the life out of the misses. The best thing out of that was she let me buy a bigger 6 metre boat to take up next year.??
Anyway good luck with you venture, you are going to need lots of it.