Absolutely, I'm glad you're planning to visit these stunning cities in Australia. Here are some travel tips for your trip:

Best Time to Visit:
In Sydney, September to November (spring) and March to May (autumn) are ideal times. Brisbane and Gold Coast are great all year round due to their subtropical climate but the best time to visit would be during the Australian winter, between June and August. Cairns, being a Tropical city, is best visited during Winter (June to August) when it's not too humid or rainy.

Route and Accessibility:
Australia has a great network of domestic flights, trains and buses connecting all these places. From Sydney, you can take a flight to Brisbane, and from there, the Gold Coast is about a 1 hour's drive. For Cairns, it's best to take a domestic flight.

Altitude and Acclimatization:
All cities are at sea level so altitude sickness is not an issue. However, it's recommended to stay hydrated, and wear sunblock due to the sunny Australian weather.

Accommodation and Booking:
Australia has a wide range of accommodations from luxury hotels, B&Bs to backpackers hostels. It's advised to book accommodations in advance especially in cities like Sydney and Cairns which can be busy with tourists year round.

Clothing and Essentials:
Pack clothing suitable for warm weather but do carry a light jacket for cooler evenings. Don’t forget your bathing suit for the beaches and barrier reef. A solid pair of walking shoes is recommended for sightseeing and hikes.

Health and Safety:
Australia is a very safe country. However, when swimming, always heed local advice about safe water conditions. Carry a basic first aid kit as some areas can have quite unique fauna.

Local Etiquette and Respect:
Australians are generally very friendly and welcoming. Tipping is not expected but appreciated for good service. Always apply sunscreen and protect yourself from the sun.