Jenni,
You could use the magic built into the ++ operator outlined in perldoc perlop. Since you have already explained what you are doing, I provide just the last step.

$array[0]++;
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If you don't want to use magic:

my ($letter, $number) = $array[0] =~ /(\w)(\d+)/;

$number++;
$number = sprintf("%.6d", $number);

$array[0] = $letter . $number;
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Those steps could be simplified, but I did them step by step so that you could see what was going on.

Cheers - L~R