There are two ways to travel from Perth to Darwin (or vice versa): per 2WD or 4WD camper. All information on this page deals with travelling per 4WD, and then mainly the Perth-Broome route.
Many parents plan for a trip from Perth to Darwin that doesn't last longer than 24 to 28 days.
Based on our own travels in Western Australia and the Northern Territory, we discourage you from travelling this vast route with children in such a short time. It makes no difference if they are older or younger, no child will enjoy spending hours a day driving. Yet, sometimes you cannot escape travelling long routes in a single day. Examples include Exmouth-Tom Price (569 km), Port Hedland-Broome (610 km) and Kununurra-Katherine (520 km). These are easy to split into 2 driving / travelling days, but if this doesn't fit your schedule all that is left is to cross these distances in one go. This is doable because you can constantly drive at 100 km/h, as you will encounter virtually no urban areas and therefore no traffic lights and roundabouts. One advantage after covering such a large distance in one day is that the long drive has brought you to a location where you can easily spend a full day (Broome) or that the next drive the following day will be a short one (from Tom Price to Karijini NP, for instance). If you are facing a long ride, let your children know that you will be in the car for quite some time so they can prepare for it. Naturally, this only goes for the older children.
One recurring theme in the feedback we receive is that families who travel the Perth-Darwin* in maximally 4 weeks have missed out on quite some nice attractions due to a lack of time. And that's unfortunate, because this is not a trip that you make every year! What we notice is that 95% of all travellers focus on the Kimberley and the Top End when they go off road driving, which is peculiar because there are plenty of other noteworthy off road destinations between Perth and Broome. Locations that come to mind include the beaches near Lancelin, Lesueur NP, Steep Point, Francois Peron NP, Gnaraloo Station, Karijini NP, Millstream-Chichester NP, Mount Augustus (Burringurrah NP), the Kennedy Range and the Carbadia-Ningaloo Road along the Ningaloo Reef. You can also make the most of your 4WD on the unsealed Marble Bar Road, which is a good alternative to the Great Northern Highway.
In our view, it is wrong to assume that the only route worth doing per 4WD camper is Broome-Darwin (or vice versa). For the route Perth-Broome* that proceeds along the above locations, we recommend that you plan for at least 20 to 22 days. It helps to know that the off road destinations between Perth and Broome are far less busy than those in the Kimberley and the Top End. If you enjoy the real off road experience combined with some more peace quiet, and if it fits your schedule, please consider visiting some of these locations. If you then also take at least 3 weeks for the route through the Kimberley and the Top End, you end up at a total travel time of 41 to 43 days. This way you get the most out of your travels and you will be visiting the very best attractions. After our final trip that we started in Perth, our 4WD camper in Darwin had 8650 kilometres on its gauge when we turned it in.
However, if you cannot exceed 4 weeks for the entire route, but you do want get the most out of your travels in the Kimberley and the Top End, then you have no other choice but to make your way from Perth to Broome as quickly as possible, whether or not via the large detour to/through Karijini NP, where you will bypass most off road destinations. We commonly see that people plan maximally 10 days for Perth-Broome* and the remaining days for Broome to Darwin. As you will understand, this is not what we prefer, but if a lack of time forces your hand, then there is little else left to do. It is also a conscious choice that we offer very little information about the Broome-Darwin route, because there is plenty of info on it elsewhere on the internet.
Finally, you might decide to travel from Perth to Broome* with a 2WD camper and then exchange it in Broome for a 4WD camper to travel to Darwin*. This is not very cost-effective, as you will be facing large one way costs. The average camper supplier will charge you AU$1000 per route and you will thus be left with AU$2000 worth of one way costs when switching campers in Broome. That money is best spent elsewhere.
*or in opposite direction.