Theme parks will be open, but they will be extremely crowded.
Absolute busiest time of the year... weather is great, school holidays for the whole country and people generally take this time of the year off work..
So they will be open, but very very busy... for popular rides i'd expect nothing less than an hours wait per ride..
Christmas , New Year and the first couple of weeks in January are extremely busy in all tourist spots (especially near the water) as that is when most Australians are on holiday. Having said that we have been to the Gold Coast many times at that time of year and love the vibe there when it is busy. If you go to the theme parks go early and line up before they open - it will be hot and crowded, but doesn’t mean it won’t be fun. No idea of your budget, but if you want to stay somewhere nice,stay at the Surfers Paradise Marriott. It is a beautiful hotel with great ocean views and a swimming pool to die for. The pool has large (I mean large) tropical fish swimming in it you can swim with and is a great experience.
You can change your dates if you like but what are your options?
All the best.