The Otway National Park is a huge park formed from the amalgamation of many protected areas.
It has a range of camping options, from bush campgrounds to coastal caravan parks and privately owned HipCamps (this affiliate link gives you $10 credit for first booking).
Camping with Dogs
While your options for camping with dogs are restricted, you do have some really nice choices throught the region. The Otway Forest Park (currently foresty land) allows dogs in campgrounds such as Lake Elizabeth (Tent Only), Stevensons Falls and Dandos, Marengo Caravan Park allows dogs all years camping and in cabins and many HipCamps, which are campsites on private land, are dog friendly (there is a dog friendly filter when searching).