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You plan and expectation is perfectly sound. Both the entire Walt Disney World Resort and the Kennedy Space Center Visitor complex are UberX areas. Walt Disney World is also an UberPool area if you're interested in sharing on the way out.
Uber does not inform the driver of your destination until they accept the ride and possibly only when they reach the pickup point so as long as Uber accepts the ride, you really don't need to worry about the driver. I've spoken to many drivers and find they prefer long rides since they pay better over time.
Plan for ~$100 each way. I've actually priced similar trips and they came in $85-$115. Keep in mind, if you request a Pool, you pay the Pool fare even if no one else is picked up. I got a $30 ride from Long Beach to Burbank that way once.
It will almost certainly be cheaper to rent a car for the day which you can do on property and very close by. Alamo has a location right at the Car Care Center. I think they have an on-request resort shuttle or you can just ask Bell Services at the Grand for the best way to get there.