"Destiny may be a clumsy swimmer, but she has a big heart. She has a big everything, actually — whale sharks are the biggest fish in the sea. Destiny resides in the Marine Life Institute, where one day an oddly familiar blue tang named Dory falls into her pool. Destiny is admittedly embarrassed by her obvious lack of grace, a product of poor eyesight (very near-sighted), but Dory thinks she swims beautifully. And Dory is delighted to learn that her super-sized friend speaks whale, too. Destiny and Dory used to talk through pipes when they were little."
She might be the reason why Dory can speak whale, even though she's not a true whale, but rather a shark.
The way Destiny jumps from her enclosure is a reference to the famous climatic scene from Free Willy.
In a different version of Finding Dory where Jenny and Charlie also had short-term memory loss, Destiny was their adopted daughter, and there would be a sibling rivalry between her and Dory.