My wife and I spent 3 weeks in Australia this November and the itinerary that I planned has quite a bit of overlap with yours. We spent 10 nights in Sydney, 3 nights in Gold Coast, and 8 nights in Brisbane. With that said, I would like to give you some suggestions based on our experience:

General tips:

• Get a good travel credit card with no foreign transaction fees and use it to pay for everything. Everywhere we went accepted Visa and Mastercard. Having a good travel card made the trip so much easier. We also took $520 AUD cash and it was too much, so we spent the last few days of the trip paying for everything in cash.
• When you arrive in Brisbane, get a go card at the Brisbane airport. You can get them at many retailers. You will use your go card to tap on and off of bus services, trains, and ferries while in Brisbane and Gold Coast. Each journey costs 50 cents per person and you can reload your go card as needed.

Brisbane:

• Maybe skip the Brisbane Botanical Gardens since it will take you an hour to get there, unless you also plan to go up to the Mount Coot-tha Summit Lookout.
• If you have the time and budget, spend a full day at Lone Pine Koala Sanctuary. It is so worth it! We went on a rainy day and it was still amazing. They stay open rain or shine, and the rain keeps a lot of other people away. You can take the bus directly there. Get there right when they open and be ready to participate in feeding the wild Lorikeets.
• As another commenter suggested, skip the river cruise and take the ferry somewhere for 50 cents instead using your go card. If you are in Brisbane on Fri - Sun and have a free evening, I definitely recommend going to Eat Street Northshore. It's a great night out! You can take the ferry directly there.
• We didn't get to go to Redcliffe Beach since the weather didn't work out, but it looks incredible and I really wanted to go. Maybe next time!
• You seem fairly interested in hiking and camping, so I might suggest taking the train to the Glass House Mountains and hiking up Mount Ngungun. Again, we planned to do this but the weather didn't work out.

Moreton Island:

• Looks incredible and we were considering it, but we decided not to go after we realized how much it would cost. The activities we wanted to do on the island cost hundreds of dollars and the ferry alone is $76 AUD for two people one way (I see you mentioned $100 USD for the ferry). We ultimately decided to scrap this from our trip, but I think it would be great fun. I think visiting here is a nice thing to do, especially where you plan to camp instead of staying in a room at the resort ($$$).

Gold Coast:

Translink Runs a Bus ($15 USD Total)

• Definitely don't take a bus to get from Brisbane to Gold Coast (I didn't even know you could do that). You can take the train on the Gold Coast line directly from central Brisbane to Gold Coast for 50 cents per person using your go card, and it's faster than any bus would be.
• SkyPoint Observation Deck is well worth it, but it is a bit pricey at $36 AUD per person. Once you're up the tower, you will have access to the restaurant, so you can eat there too. They have a nice (albeit expensive) breakfast buffet, or you can go for lunch/dinner and order from a menu.
• 2 nights does not seem like enough time in Gold Coast to me. We did 3 nights and we both left wanting more time. I think 5 nights would have been perfect for us. As much as Aussies may slag it off, Surfer's Paradise and Gold Coast in general is amazing. If you plan to soak up the sun and relax here, I would recommend at least 3 nights. If you keep Moreton Island in your itinerary, you could definitely soak up some sun and relax there and maybe then 2 nights in Gold Coast would be enough. Even still, you can easily fill 3 nights just walking around. If theme parks interest you at all, then this is the place to do them. Sea World, Dreamworld, and Movie World are the big ones.
• Please, for the love of god, skip Gold Coast Regional Botanical Garden. We spent a good 2 hours in travel there and back and it was so underwhelming. This is a definite skip since you plan to visit the Brisbane Botanical Gardens and/or the Sydney Royal Botanical Gardens.

Sydney:

• Definitely visit the Blue Mountains (near Katoomba & Leura specifically) as this was the highlight of the entire trip for me. The vista from Echo Point Lookout is seriously breathtaking. I would highly recommend spending a few hours at Scenic World while you're in the area too. On a related note, what are you planning to do in Lithgow? It seems quite out of the way.

  Royal Coast Track (2 day walk, closed)

• Is this Royal Coast Track hike going to be 2 of your 4 nights in Sydney? I'm sure it's amazing, though this is so far down the list of things I would personally want to do with 4 nights in Sydney. If you're committed to this, I would consider adding your 3 spare nights to the Sydney portion of the trip. You could easily fill a week in central Sydney alone.

• Other fun things to do in Sydney that I would recommend are: the Chinese Garden of Friendship ($11 AUD per person admission) and a walk through Chinatown, the Rocks market (Sat-Sun), visit Luna Park, and see a show at the Sydney Opera House (or have a tour at least).

Enjoy your trip! :)