There are a number of shuttles from the MCO to Port Canaveral, Go Port Canaveral is one (they also arrange hotel/shuttle combos if that interests you), of course RCL has their own shuttle (usually costs more), Cortrans is another that is recommended (I have used it and it was really good both to and from the airport, actually they will pick up at various airport hotels too). Cocoa Beach Shuttle is another one, they will take you to hotels in the Port Canaveral/Cocoa Beach area as well. They will also give quotes on picking up and/or dropping off at Disney properties (but it's not cheap lol).
I've used Cortrans and Go Port Canaveral, both worked well with no issues. GPC is a bit cheaper I believe.