if you remove as much of the living things as possible, and drain all the water, you could probably get away with keeping your carpet plants if you cover them with wet towel/paper towels, as wkndracer suggested. i made a 3000 mile move with a planted tank, and i can tell you that any amount of water in it will beat the crap out of the plants. that said, the dwarf hair grass was the only plant that seemed to make it through with little damage. the substrate did accumulate around it and it was quite buried when i reached my destination.
my only substrate was sand, so it was easy for me to excavate the hair grass once i got where i was going. the rest of my plants ended up as a plant salad, thousands of little pieces that i had to grow out again.
also, if you move any tank with water in it, turn it so that its widest sides are facing front and back of your vehicle. that will give the water less room to move, which will make a HUGE difference. if going long distances (like i did) put a lid on a bucket, punch holes in it, and add one of the battery powered bait saver air pumps you can get at a bait shop. then fill the bucket most of the way with water. the lid will keep it from sloshing out too much, and filling it up nearly to the top will keep the water from being able to move around too much and beat your fish to death. things will get a bit wet around it, but its the safest way to transport your fish and shrimp long distances.