What details support a prediction that Squeaky will be tough to beat in the race?

The last part of the second paragraph includes a nice detail that alerts readers to the fact that Squeaky is a fast runner. 

And as anybody can tell you, I’m the fastest thing on two feet.

Squeaky tells readers that she is the fastest thing on two feet. In order to make such a claim, she would have to be fast, and she tells readers that other people will support her claim.
The third paragraph is probably the best location for details regarding Squeaky's speed. She starts the paragraph by telling readers that there has never been a race that she has entered that she hasn't won.

There is no track meet that I don’t win the first-place medal.

Next, Squeaky lists out each of the race categories that she has won over the course of various years. My favorite detail is when she tells readers that she plans on winning the entire relay race . . . by herself.  

And tomorrow I’m subject to run the quarter-meter relay all by myself and come in first, second, and third.

Older kids call her "Mercury" because she is so fast. Squeaky has to be quick if she is deserving of the name of the winged messenger of the gods.