You cannot move your equipment from your old ship to your new one. You have to equip it with its own equipment. If you're in need of money, you can sell off your old ship's equipment to get crystals to buy the new ship's equipment. But be warned, the starter ship you get costs no crystals to repair, while all other purchased ships do cost crystals to repair.
I'd recommend leaving your starter ship fully-equipped, and save up crystals to buy the new ship equipment.