After this obligatory warning of the hazards and potential fragility of regular expressions, you can fix your case fairly trivially by moving your hyphen into your capturing parentheses:

/("[^"]+|-)/

You can also use non-capturing parentheses ((?:...)) with expressions of the form:

/((?:"[^"]+)|(?:-))/.

You also might want to add a close double quote to your regular expression, so you don't match incorrectly on "A string" not a string "a string", a la

/("[^"]+"|-)/

See perlretut for more information.