I've always taken it that the mouse character, Jerry, was male. This spelling was usually the one for men, and the way in which the character is drawn looks more male than female. A female cartoon mouse would have large eyes and longer eyelashes, and be more coy than this.
Jerry Mouse is male. "Jerry" is short for "Jeremy" or "Jeremiah", which was the name of an Israelite prophet. The name is common in both Britain and America.
Recently, especially in America, many girls have been given male names. "Jerry" is an example of a name that can now be given to girls: a famous example is Jerry Hall, who was once Mick Jagger's common-law wife.