Hi Laura
If you can clean the filter a week or so before you move, it will help. Then when it comes time to move put the filter materials in a bucket of tank water with an airstone bubbling away. They will last all day like that.
Also if you can do a gravel clean a few days before moving it will make life a bit easier.
Don't feed the fish on the day before you move. This will allow them to get rid of all the waste from their system and they won't foul their transport water as readily.
Turn the heaters, lights, etc off and drain the tank water into 20litre water containers, (available from the hardware). Put the fish in a bucket of water and the plants in another. Try to have an airstone bubbling away in the bucket/s with the fish.
Get as much water out of the tank as possible. You can usually leave the gravel but if there is a lot it might be easier to move the tank without the gravel in it.
When the tank is put in the car make sure it is well cushioned under the base.
You can buy Power Inverters from automotive stores. These plug into the cigarette lighter in your car and convert the 12V DC from the car into 220V AC (whatever the voltage is in your country) so you can run normal electrical appliances from it.
They are available in different wattages. A 75w power inverter is usually fine to run a couple of airpumps for the fish in the buckets.
You can also use a battery operated air pump.
When you have set the tank back up after the move, keep the feeding down for a week or so and monitor the water quality.