I suspect that the uneducated rats were sent to visit the snake exhibits.
If memory served, it was a "great white whale from Labrador," meaning that it was likely a beluga, which are pretty small as whales go.
When I was a kid, I saw the original Jumbo the elephant, skinned and stuffed and in the middle of a museum of circus memorabilia at Tufts University in Medford. Massachusetts, shortly before the museum burned down, taking the stuffed elephant with it (his skeleton and heart are in other museums). I remember thinking he didn't look all that big to me (shrinkage!) and at 5 feet tall, the top of my head came up to about his "elbow" where his front leg met his body. His trunk was full of coins, because apparently the students used it as a sort of wishing well before exams, and his tail was held on with tape, because apparently someone had tried to use it as a rope swing at some point. It was kind of sad, actually. The Tufts sports teams are still called "The Jumbos."
There is a Barnum Museum in Bridgeport, Connecticut, but I've never been. I also liked the 1980s Broadway musical Barnum with Michael Crawford, which is in its entirety on Youtube somewhere.