Consistency is key
Moving fish/Amphibians is always going to be stressful for them. The best thing you can do to ensure that they are stressed as little as possible is to keep the conditions as similar as you can during the transport and beyond.
Your key question is about the process of re-cycling the existing tank after the move. This shouldn't be necessary assuming that you take the necessary steps to ensure that your filter media (really the beneficial bacteria that lives on it) is not adversely affected.
To my knowledge there are not a lot of things that differ between moving an Axolotl and a fish so let’s take a look at the process that I would and have followed in the past:
Do your homework
- Plan your journey from the old location to the new one (avoid a road where your fish are going to be bounced around that doesn't gain you significant time).
- Are you likely to get stuck in traffic? (You said it’s an hour long journey, could that easily become 2?)
- Is there a 'good' time of day to do this at (early morning/ late evening when traffic is minimal for example)
- Is it easy to get the tank in and setup ready for the axolotl or will it take some time?
- Are you going to need help moving the tank? Rope in some others to help you out.
- Is the temperature going to be drastically different to the regular water temperature? Cars can get warm in the sun, try to keep temperature fluctuations to a minimum.
This might sound a bit overkill but if your journey could suddenly double in length, the last thing you want is your pet paying the price for it.
The Move
As ever, the smoother you can make this transition, the better for the Axolotl. Be very careful when moving a tank which has water in [1]. As you say, you’ll want the absolute minumum water in it as possible because without the stand bracing the tank in the correct place you may find that it cracks. In the case of an external sump filter [2], you may be able to completely drain the tank and just keep the sump filled with water instead. Either way, keep the filter full submerged or your bacteria may die off.
If you have tropical or marine fish, you would need to be more aware of the temperature because it’s harder to keep water at greater odds to the environment at the same temperature (see Newton’s Law of Cooling for more information).
You’ll want to move as much of the aquarium water as you can to the new tank location for two reasons; firstly, if the animal is already acclimatised with this water, that will be one less ‘new’ aspect for it to get used to and secondly; if you move water that you already know is of ‘good quality’, it reduces the number of variables if problems arise later on. Check the parameters of the water at the new location to ensure that they are not drastically different to what the Axolotl is used to. If the water parameters change quickly in the new location this could cause health complications.
You could also place the axolotl in one of the containers because the more water you transport your axolotl in, the less impact the waste it produces will have on the quality of the water and the slower the water temperature will change in relation to its surround environment [3]. If you can use an opaque container then that’s even better because most aquarium animals will simply go to sleep as if it were night time (excluding nocturnal fish).
It all boils down to: “As quickly and safely as you can make it”.
Settling in
It goes without saying that once the move is complete, you’ll need to keep a careful eye on the parameters of your tank and if there is any spike in Ammonia or Nitirite, you’ll need to deal with it fast or the Axolotl will suffer. As I said above, check that the water in the new location is similar to the old. If it isn’t, gradually transition to the new water but allow time for the inhabitants to get used to it.
Summary
I know I keep repeating this, but ‘easy does it’. The Axolotl will be much happier if you ensure there is as little change over the journey to it’s new home as possible. Of course you can just put it in a box and take your chances, but stress is one of the biggest killers in aquarium fish and whilst they might not die because of the journey, it could see a decreased lifespan.
The steps suggested above are ones I followed when moving my Tropical Community tank from one flat to another (30 minutes away, 2 flights of stairs) and I was very glad I’d planned it in advance to avoid making what can be a difficult task into a nightmare for the fish and I.
1: Can I Move a Partially Filled Aquarium? - The spruce
2: What is an external sump filter? - OscarFishLover.com
3: How does cooling scale with volume? - physics.stackexchange.com