A problem with your current regular expression is that [^" ]+ does not allow spaces.

This fails for example for the following string, which I think should be valid:

Corion says "hello sarathy"
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If you want to stay with your approach of matching the tokens (words or quoted parts), I suggest reading perlre, especially on alternation.

For such an approach, I would restate the problem as Match every token that starts with a letter and consists only of letters, or starts with a double-quote and consists of non-double-quotes..

UPDATE

You can parse the strings with Text::CSV

#!/usr/bin/perl
use warnings;
use strict;
use Text::CSV;

my @strings = (
    '"my" "dog"',
    '"my" "dog shepherd"',
    'my dog',
    'my "dog shepherd"',
    '"my "dog"',
    'my "dog shepherd',
);
my $csv = Text::CSV->new ( {sep_char => ' '} )
    or die "Cannot use CSV: ".Text::CSV->error_diag ();

foreach my $string (@strings){
    open my $fh, '<', \$string or die "Cannot open string";
    if (((my $temp = $string) =~ tr/"//) % 2){
        warn "invalid string";
        next;
    }
    my $row = $csv->getline($fh);
    if (!defined $row) {
        warn "getline failed";
        next;
    }
    close $fh;
    $" = ' | ';
    print "@$row\n";
}
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