From the "Perl Cookbook", recipe 3.2: Convert your dates to epoch seconds and see if current time is between them:

use Time::Local;
my $time1 = timelocal($sec1, $min1, $hours1, $mday1, $mon1, $year1);
my $time2 = timelocal($sec2, $min2, $hours2, $mday2, $mon2, $year2);
my $now = localtime;
if ( $now > $time1 && $now < $time2 ) {
    # do stuff if within range
}
else {
    # do stuff if not in range
}
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