You really don't need travel companies, you can sort it yourself. We did a three week reccie trip before we emigrated and I halved the prices quoted by travel agents for a lot of things. Definitely plan early though as it is peak season here (I'm in Sydney).
First thing, look at flights. Are you interested in adding a night or two stopover on the way home? If nothing else it breaks the journey so the jet lag isn't as bad if you are heading straight back to work. I always try and stop in Singapore as I really like it (as do my kids), but that limits my choice of airline. Etihed were doing a great sale recently but they fly through Abu Dhabi.
How old are your kids? That will determine the kind of things you might want to do/see when you get here. Then, what kind of holidays do you like - chilled with not too much extra travel or organised activities and busy busy.
Next, are you staying with family? You say they have a house full, are there other people coming and if so is the expectation that everyone stays - how realistic is this? Most of my UK friends here spend February trading stories about CF guests and as I have mentioned on here before 2017 will always be remembered in our house as "the year the X family ruined Christmas"........ Arrange your own airport transfers (most people don't really want to meet the 5am flight), hire a car if you need to, share costs and the workload of having people staying. Airbnb have some great places to stay here so think about breaking it up a bit if you are staying with family. If you need accommodation for your whole stay I can come back to you with ideas.
Once the basics are sorted you can fill in the gaps. As someone else said Melbourne is fab, and if you have older teens/young adults like we do and want nice restaurants, shopping and a cool city vibe it's great. There are definitely more "Australian" experiences though. You also need to thing about are you flying in and out of Sydney so if you go somewhere else you will have to come back for your flight, or do you want to fly back from somewhere else. Don't underestimate the distances here, it still blows my mind that when we fly to Bali most of the flight is spent over Australia. Just had a thought - the London/Perth direct flights start this weekend, not sure if that is if interest.
Ask away if you have any more questions, I have a lot of free time on my hands at the moment 