The link that bonger has provided covers Inskip Point peninsular dea and is the only place to camp right on the beach that is pet friendly. And dogs must be leashed at all times....the rangers get a bit peeved if they find them not tied up.
Make sure you get your permit before hitting the any of campgrounds, it is available online or from the QPWS office as you enter Rainbow Beach.
There are some camping areas near to the toilets and you can use a gennie and have a campfire presuming there are no fire bans. You need to take in your own firewood.....not allowed to collect any from there.
There are no showers unless you drive into Rainbow Beach where you can have a cold shower at the amenities block on the main beach. Of course you can take your own or dig a latrine.
Water is available just of the outskirts of town as you head out to Inskip. An ice/bread man/woman comes around twice a day in holiday time....not sure about other times.
There is an iceworks in Rainbow Beach where you can buy bulk ice really cheap.....but you must take your own container......$10 for 10 kilos from memory.
The worst day camping still beats the best day working