I drove the Patrol from Cairns to Cape York in '02 towing a Kimberley Kamper. Went up through the Daintree to Cooktown, then inland to Lakeland before heading north through Laura.
Did it in June and it was the hottest, most humid June they had ever had. It was 38 degrees with 90% humidity. In the walk from the carpark to the tip and back we each drank 2 litres of water - the walk is over rocks but less than 1.5km.
On the car, we broke the CD player and welds on a steel roofrack with the corrugations.
Is my trip related to cycling? Nah!!

But it does show that even if you go in the coolest month historically, it might go pear shaped. You will ned to carry a lot of water.
There are some nice waterfalls and rivers just of the "main" road which are worth stopping at and, if you can, camping. Camping at the Laura campground is fine, are are the other petrol stops (names escape me atm). There is quite a distance between official stops though so be prepared for bush camping.
I am pretty anti Lakeland, but we may have just hit there on a bad day!! It was the day before the rodeo and the road into town was lined for about 1km with trophy boar. Yes, they were displaying wild pigs they'd shot. Stunned me.
Trip up through the daintree has a couple of river crossings that you may prefer to walk through. There are some pretty big hills too - it is all gravel except there is a very steep bit over the Donovan Range that is actually sealed it is that steep. Couple of hills around Laura and a couple of dry super crap river beds to cross
On the road to Weipa before the turn to the cape, it is often a race track. We saw some shocking driving and you may be peppered with gravel from speeders. It is a wide road, but it won't matter. The road is pretty sandy after the turnoff and bumpy and narrow. Because it is so bad, 4wds will do about 60-80km to ride the corrugations. This may make it dangerous on a bike so take care on the single lanes.
In saying this, you might not see a car

We were pretty early in the season I believe, so traffic was pretty light, but we saw enough. Prepare for the traffic but don't count on it in an emergency.
If you make it 20km from the top, you cross the Jardine River. Big wide thing with a ferry that transports you. When we did the trip, it cost $100 to make the journey (they throw in the return for free). Not sure of the bike price, but it will be way too much. Apparently, you used to be able to cross a little further up from the official crossing, but the locals dynamited the river to force people to take the ferry
Most importantly, take a fully stocked first aid kit and make sure everyone knows how to use it. You just never know. Also be prepared for heat exhaustion - just in case.
Sorry this hasn't been cycling related, but I hope there is a bit here that you can use.
