They don't seem finicky, but they are. A move can be traumatic for a plant. So you need to handle the situation very carefully. If your plants are in ceramic planters, it's best to move them to plastic planters a few weeks before the move. Plastic planters are much lighter, and you can pack up your ceramic planters to be sure they don't get damaged during the move. You'll want the plant to get used to the plastic container well before it's moved. Plants also need to remain in a temperature-controlled environment. So putting them in the back of a moving truck for days on end in 100-degree-Fahrenheit (37.7-degrees-Celsius) heat is not a good idea. Put the plant in the car with you where the temperature is just right.