This is something that has been brought up on the air more than once in the past week. How is Mr. Krab's daughter a whale? Here is what I was able to find by going to Pearl Krabs wiki page.

Hillenburg often received letters that asked why Pearl is a whale while her father is a crab.[3] The answer is simple: Hillenburg wanted each member of the main cast to be a different animal.

Hillenburg, being Stephen Hillenburg, who created Spongebob. But there's more to Pearls' story.

The in-universe difference in species between Pearl and Mr. Krabs has never been addressed in an episode, but the official trivia book states that Pearl takes after her unseen mother, who was also a whale. Stephen Hillenburg was strongly against revealing the identity of Pearl's mom and kept it a secret throughout the show.[4]

So there you have it. While it's never been addressed on the show, it has been answered. Pearl takes after her mother. How did Pearl Krabs get her name?

Pearl was named after the phrase mother-of-pearl, a common term for the inner layer of some sea-dwelling mollusks' shells. Her lack of a mother is a reference to the phrase as well.