Definitely - without hestation - use a TAXI.
Call your CBR front desk CM's the night before and ask for a taxi from CBR to the Beach Club at 7:30 AM. You will pay about $10 with tip, well worth it, for door to door service. You will be at the BC by 8 AM. They have a very nice gift shop to check out.
You will be less stressed and enjoy the Cape May Buffet and characters in beach clothes.
After breakfast, I would suggest either walk or boat to EPCOT or boat to DHS. The friendship boat to the parks will be a nice way to end your breakfast.