I don't think seeing a bit of both Australia and New Zealand is unreasonable or impractical, you just have to limit your vacation to two or three places. It just depends on what you hope to see and do, and what your budget is. You are never going to see all the highlights of either country in two weeks, so just figure out what you most want to see and do. Sit down with all your friends and look over a couple of guidebooks with lots of photos of the two countries or checkout some websites together.
Even if you were to spend all two weeks in Australia, you would see relatively little as the country is so large. For instance, the flight from Sydney to Perth would take about 4.5 hours, the flight from Sydney to Darwin would take almost as long. On the other hand, the flight from Sydney to Queenstown, NZ, would take about three hours.
You could spend your entire two weeks just exploring the South Island of New Zealand, but you'd be driving around from place to place to see as much as possible and you'd be moving house every night or two.
Both Air New Zealand and Qantas offers package trips that would allow you to spend a few days in Australia and New Zealand that would give you a few nights in a few different places:
I don't know your friends, but if I were traveling to both countries with a group of my friends, I would probably rent vacation homes in two or three different places that would serve as good bases to see the surrounding areas. It would take more organizing and coordinating, but in the long run, you could come up with a trip that was more tailored to your specific needs and interests. For instance, you could rent a holiday home (that sleeps 10) for a week in Queenstown, rent another holiday home for a week in Sydney or Cairns/Port Douglas (they are about an hour apart), or maybe two days in Sydney, four days in or around Cairns/Port Douglas. You'd spend probably around US$1800 on total airfares (including those from the US, if that is where you are coming from), but you would probably save by jointly renting a hoiiday home, which would also give you the option of eating in. Dining out can be costly in NZ and Australia. You'd have a place where you could all socialize, instead of having to go to some bar or restaurant or crowd into each other's hotel rooms.
You could make a lot of day trips out of Queenstown or Cairns/Port Douglas. In most cases, you'lll want to rent a van or a couple of cars to get around.
From Queenstown, you could visit Wanaka, drive a bit on Haast Pass and into Mt. Aspring National Park; see the nearby towns of Arrowtown and Glenorchy (whch are in different directions), go wine tasting in the Central Otago (Gibbston Valley, Bannockburn, Cromwell), and spend quite a bit of time doing things in Queenstown itself, gondola, jetboat, bungy, Queenstown bike trail, etc. There are bus tours that will take you to Milford Sound and back in a day, which include the Milford Sound cruise and some stops along the way, and will even give you the option of taking a scenic flight back. The drive is a long one (4.5 to 5 hours from Queenstown to Milford Sound) so I don't think you'll want to do this drive yourselves (too much time in the car) unless you do an overnight cruise on Milford Sound, which can be lovely. The overnight cruise includes dinner and gives you a chance to kayak or take a boat trip onto the sound when it is so quiet and calm. In the morning, you'll get back to the dock early with enough time to slowly make you way back to Queenstown. You can even stop for a hike along the way. I suggest the 3-hour round trip hike to Key Summit from Main Divide parking (the start/end of the Routeburn Track). Definitely stop at Mirror Lakes (very little walking required) and the Chasm (15 minute walk), both off Milford Road. Milford Road is gorgeous.
From Cairns or Port Douglas, you could make a trip out to the Great Barrier Reef to scuba or snorkel, take the Skyrail or Kuranda Railway, see an Aboriginal performance. visit the Daintree Rainforest and Cape Tribulation.
There are so many things you can do and see in Sydney and you wouldn't need a car.
The other thing you should consider is the weather. The wet season in Tropical North Queensland begins in November. Supposedly, this is when the weather starts to warm up and dry out on the South Island of New Zealand, but not necessarily. Last summer, there were horrendous storms on the South Island that led to road closures and emergency rescues. A bridge on NZ's West Coast was washed away.
As for seeing a bit of two countries in two weeks, I don't see this as an issue. A lot of folks vacation in Hawaii, or in the South Pacific, or Asia, before continuing on to NZ or Australia. Here in NZ, where I live, I meet a lot of folks who have been to the US. It's not unusual for them to fly San Francisco to Las Vegas to New York. Or to from Los Angeles to Texas, or wherever. On many of my trips from the U.S. to Australia and NZ, i have often vacationed in Singapore, Indonesia, Malaysia, or the South Pacific along the way.