Aquariums are different sizes but you should plan on at lease 2 to 4 hours. You could visit the fish and crustaceans first followed up with the cake and present party. If there is a picnic area at the aquarium, the cake and presents can be held there. You'll probably want to plan on storing gifts, food and desserts in an ice chest in a car or van until after the aquarium visit, unless the aquarium has a place for you to store it. When having an off site party, be sure you have phone numbers and extra automobile room for attendees just in case a parent gets stuck at home or in traffic.
Most aquariums offer special rates for children and group packages that are very reasonable.
Some offer special party and sleep-over packages. My son attended a sleep-over party at the Long Beach Aquarium of the Pacific and slept within five feet of the tank. Cards that look like fish, starfish, clams, whales, etc.