Port Campbell is a good base as stated for the 12 Apostles, London Bridge, Loch Ard Gorge etc if you can find somewhere to camp with a dog. I don't think they are allowed at the caravan park. We also stayed at Johanna Beach camp ground for a few nights. Great national park (free) camping area with "nice" toilets (not smelly at all) but no water etc - be self sufficient. (Dogs on leads are allowed at Johanna) From this base, we explored the area a bit, including the Otway Fly.
Also stayed at Kennett River Holiday Park and did a couple of day trips from there. A very nice spot with plenty of koalas at the back of the park. (just look for all the tourist mini buses each morning - cant miss them) Unfortunately no pets allowed - the same for the Big4 at Wye River ( I assume due to the koala and other native animal population)
Out of interest, not having travelled the GOR for many years, we decided to stop at most memorials and/or historical markers along the way. The information on the area was fantastic and well worth "continually" stopping.
And yes, to visit the Cape Otway Lighthouse (read get anywhere close to it - you cannot see it from the carpark), they sting you $18.50 each. We walked up to a "lookout" where you can see some of the lighthouse in the distance !! A reasonable drive to get to it from the GOR, but there are/were plenty of koalas to see and photo opportunities along the way.
All the best with it. The GOR is a great drive and a beautiful place to visit. As said, you could drive it in a day, but then you would miss out on heaps.
Cheers,
Dave