They'll stay clean and won't get crushed. To save time, rent a carpet shampooer at the same time you rent your truck. Mark each box with its contents and destination room. That way, you and your helpers will know where each box belongs at your new home. If moving locally, you may want your pets to spend moving day with a friend.
Animals can become confused and frightened during a move.
Load houseplants last and unload them first. Inc. All others are the property of their respective owners.