You'll need to escape it, even in a character class; otherwise it will think you're trying to escape the
var validID = regexp.MustCompile(`[\\]`)
But for that matter, you can just get rid of the character class entirely:
var validID = regexp.MustCompile(`\\`)
Also note that the string
"I have Hello \"World\"" does not actually contain any backlashes.
\" is an escape sequence a double quote. If you want to create a string with backslashes use:
str := "I have Hello \\\"World\\\""
str := `I have Hello \"World\"`
A working demonstration can be found here.