Australia Tours

Australia is big. It would be like asking are there any must see in the USA. IMHO must see would be Sydney and Melbourne. Several years ago we went there. We were 5 friends and had 3 weeks. We rented a car and spent one week in Tasmania and 2 weeks driving from Melbourne to Sydney stopping on the way. Highlights: Thredbo in White mountains - winter and summer resort. From there we conquered Mt.Kosciuzsko, the highest mountain of Australia.
Numerous wineries
Canberra the capital
Beach towns
Sydney - one of the most beautiful cities in the world
I don't have personal experience with guided tours in Australia. I would suggest search for it on internet. I just did that for New Zealand and they were plenty.

We have been to Australia twice and loved it. Very easy to do one your own, but if you would like a tour, you can indeed find a number of them. Since you specified a small, active group I checked the "usual suspects" like Backroads and Active Adventures, but they don't cover Australia. One I did find is this one with OATS (Overseas Adventure Travel):

https://www.oattravel.com/trips/land-adventures/south-pacific/ultimate-australia/2016

They start in Melbourne (a beautiful and fun city) and end in Sydney (world-class), visiting Alice Springs, Uluru, and the Great Barrier Reef on the way. These are five of the "must sees" on most lists of what to see and do in Oz, so it looks like a good trip. I have no experience with this company but they do get good reviews.

Road Scholar offers a more "off the beaten path" active trip that includes Tasmania and the Great Ocean Road (near Melbounre). But they are aimed at A certain demographic---seniors--- and I don't know if that is your age group.

Gadventures.com seems to be aimed at a younger group. They act as a booking agent for a National Geographic Journey that includes Sydney, Port Douglas/Cairns up north, Uluru and Alice Springs in the center, and ending at Melbourne. So fairly similar to the OAT trip for a bit more money.

Thanks Ilja and Lola. Looks like I better do my homework. I am very familiar with Europe, but not so much with Australia. My oldest daughter performed in the opening ceremonies for the 2000 Olympics. We couldn't afford to go at that time, but have always wanted to go.

I guess it depends on amount of time, budget (can you afford to fly between a dozen different destinations or are you restricted), time of year (not much point going to Whitsundays in the middle of summer if you like swimming) and interests. I live halfway between Sydney and Melbourne so dont particularly consider myself biased. Personally I love to visit Melbourne - Melbourne is a cool city, but I guess for iconic places, you would look at Sydney, Northern Territoy, Queensland Coast. I love Tasmania, but would only add it on if you are specifically interested in scenery, walks and long drives and have plenty of time.

Your best bet is to collect several guides to do some homework and cross-check your specific interests against the time you have available.
You could probably travel independently and put together an itinerary with destination-specific tours for a lot less than the all-inclusive tours you may find online...most of which don't include airfare.
For example, find a nice apartment in Sydney for 5-7 days, use public transportation to explore the beautiful city and its suburbs, and book day tours with local providers for nearby attractions like the Blue Mountains and Hunter Valley. Can do the same sort of thing in Melbourne, booking a day trip out along the Great Ocean Road - although I'd personally recommend a car for the extra freedom of movement one will provide. We've had good luck using the Trip Advisor "things to do" feature to help us with our own trip research.
For a taste of the Outback I'd recommend Alice Springs and/or Uluru. Qantas runs a low-cost subsidiary within Australia call Jetstar that provides convenient, cheap (though spartan) air connections to just about every tourist attraction within the country - especially if you plan and book ahead. Other possibilities would be Cairns (for the Great Barrier Reef), the Gold Coast and Surfers Paradise near Brisbane, and the pretty little city of Adelaide.
Recommend booking the trip as an open jaw, maybe flying into Sydney and returning via Brisbane - which would prevent wasting a day having to backtrack to catch your flight home.
Don't forget to purchase your Electronic Travel Authority (ETA) visa just before you leave. They cost about US$15 as I recall.

I visited Australia (twice) and New Zealand with Adventures Abroad. Groups are small, tour leaders excellent. web site adventures-abroad.com

In fact, there’s so much to say about Australia. Australia is truly a land of diversity. Australia’s cities are buzzing.
The Kimberley in the northernmost corner of Western Australia is savagely beautiful. I was also impressed by the Pink Lake.
Gawler Ranges in South Australia also one of the most astonishing scenery. Kangaroo Island is worth visiting for a few days to experience as much as possible.