Based on your itinerary I could answer you more precisely.
I did many trips through Namibia and Botswana. What makes a huge difference is where you're going and for how many days you won't come across anything, not even a fuel station with a small shop. Botswana is tougher in this regard. During my last trip I had to cater myself for up to 10 days with your same setting: toyota hilux double cab and 40l fridge. I made it with no issues but was alone. Having no chance to buy anything, what occupied most of the space was water and woods. Assuming you'l do a classic tour in Namibia, there is a good chance that at least once a day you come across a fuel station where you can always find drinks, and in most campsites you would find wood to buy at receptions. So when you stock-up you rather focus on food while you can stay lighter with water and woods as these can be easily found all around at the small shops on your way. You use the 40l fridge to keep meat, cheese, butter, milk while the drinks can stay in the ammo boxes or just back in the canopy. Veggies can also stay in the ammo boxes and rolled in newspapers. As long as you keep veggies and fruits in a closed area with no direct sunshine, things like potatoes, some salads, onion, garlic, carrots, broccoli, apples ect. will last for up 1 week. So if your plan is on a 3 days basis I'd say you can pretty much buy whatever you want as long as you're skilled in space management. As Joachim said, tins, rice and pasta will last forever, do not need a fridge, and relatively cheap in space. The problem of being 4 people is the luggage. While I had only mine, you will have at least 4 and that makes obviously a huge difference a part from having to buy food for 4 people.
If I had to plan a 10 days no-nothing stretch, for 4 would be impossible in one vehicle with no trailer, so would split in 2 cars. But if you're not going crazy in terms of "out in nowhere" it could work since you could stock up in water and wood every day.
Your packing skills will be challenged, but once you get the vehicle and with a good teamwork, I think it's doable. I've seen many double cabs with 4 people an RTT along the way...which does not necessarily mean they where camping all the time, perhaps they had the tents for just 4-5 days out of a 2 or 3 weeks trips, so they didn't have to manage the space that much.
So it really depends on where you're going and for how many days you won't come across anything. In Namibia this rather happens deep in Kaokovled in the north or off the beaten roads in Damaraland.
For the kind of travel I do, your configuration would be impossible for me. To mange 4 people to be catered for 10 days, I'd need a trailer. But this doesn't seem your case so...
If you stop for 2 nights in Windhoek when you arrive, take the time to know your vehicle and your configuration the next morning, and then go shopping. A menu plan you agreed in the family for the 3 days will help you to do the shopping accordingly. Teamwork will be a key word.
