If you use the disney transportation, you can leave your bags in your Hyatt room and bell services will send your bags to the ship and they will appear in your stateroom. For a family of 5, it was exactly the same price using Disney Transportation one way vs. using Happy Limo (we used them on the way back) and tipping the driver.
Uber XL one way to the port from MCO would be about $115, but they would have to pick you up off of airport grounds.