You could separate out the datetime section using s/// before you split:

use warnings;
use strict;

while (<DATA>) {
    if (s/(\[.*])//) {
        my $dateTime = $1;
        my ($remoteIP,$rfc,$userID,$requestType,$statusCode,$sizeOfFil
+e) = split;
        print "$statusCode $sizeOfFile\n";
    }
}

__DATA__
66.249.65.107 - - [08/Oct/2007:04:54:20 -0400] "GET /support.html HTTP
+/1.1" 200 11179
[download]