Because they are living things, plants are considered perishable and need special handling & care to prevent damage during transportation. They need air, comfortable temperatures, and adequate humidity. For these reasons, most insurance will not cover any loss or damage to plants.
If moving state to state, find out if plants can cross state borders. A few agricultural states have strict rules about bringing plants within their borders. Florida and California, for example, grow valuable cash crops they want to protect from bugs or disease that may be on plants you bring with you. Be prepared to be asked about plants and fruits in your vehicle.
Be prepared for restrictions! Call your local U.S. Department of Agriculture to check on regulations.