Why is Squeaky compared to quicksilver?

There are two reasons why Squeaky might refer to herself as "Miss Quicksilver." The first is as a reference to her speed in the fifty-yard dash. When Squeaky uses this nickname she does so proudly, and perhaps to boost her own confidence, by reminding herself of just how quick she is.
The second reason for the comparison is to reference Squeaky's volatility. This is probably a reference that the author is making, rather than a reference that Squeaky is herself aware of. Throughout the story, Squeaky comes across as a rather volatile, temperamental character. For example, if somebody teases her brother, Squeaky's response is to "knock (them) down and take (her) chances." And when she and her brother are approached by "Gretchen and her sidekicks," Squeaky says that she's "ready to fight, cause . . . I much prefer to just knock you down right from the jump and save everybody a lotta precious time." Quicksilver, or mercury as it is also known, is a very volatile metal, meaning that it changes its form more easily than other metals, echoing how Squeaky changes her mood very easily.
Therefore, "Miss Quicksilver" is a fitting nickname for Squeaky because it alludes to her speed in the fifty-yard dash and also to her volatile temperament.

Squeaky is the narrator of the short story "Raymond's Run" and refers to herself as the "fastest thing on two feet." Squeaky is an excellent runner who consistently wins first-place medals at track meets. At the beginning of the story, Squeaky says that the older kids gave her the nickname Mercury because of her natural speed. Mercury is the name of the Roman god of travelers and transporters of goods. According to Roman mythology, Mercury is also the fleet-footed messenger of the gods and is often depicted wearing winged sandals, which help him run faster. After Squeaky and Raymond run into Gretchen and her friends strolling down the street, Squeaky refers to herself as "Miss Quicksilver" when she walks away. Quicksilver is liquid mercury and is often used in similes and metaphors to describe something that moves or changes very quickly. Squeaky is known for her speed and is already called Mercury by the older kids, which is why she refers to herself as "Miss Quicksilver."