Kangaroo Island and Camping with a dog

Gday all,
We are thinking seriously about taking the camper to Kangaroo Island over the Xmas break, leave 25th return back around the 4th of 2010,
We have been there many times and stayed in great houses and have done all the touristy things but this year really want to go again,especially now having a Poptop camper and the landcruiser recently purchased.
I have heard that Camping is even better , so please get back to me with some camping with a would suit ,unpowered doesn't bother us to much as we have catered for that.
BUT AND A BIG But,
Is we have our dog to cater for being that she is part of the family, I have heard and know, that in national parks that dogs are not permitted and can incur a fine ,so which means Flinders Chase is out , but I understand the locals are an issue?
We are very responsible dog owners and don't let it of the lead unless we have ensured all ok,I am also aware of the penguins and wildlife issues with dogs, this is why I am inquiring on this site
as I am sure other dog owners have the same problems,
Another issue is we like our space and don't really want to be bundled up in a overcrowded caravan park, over Xmas with thousands well hundreds of others.
so suggestions would be great.
cheers to all
wizzwozthere