RMcLeod answer is OK, but I'd suggest you extracting this as a custom rule:
Validator::extend('olderThan', function($attribute, $value, $parameters)
{
$minAge = ( ! empty($parameters)) ? (int) $parameters[0] : 13;
return (new DateTime)->diff(new DateTime($value))->y >= $minAge;
// or the same using Carbon:
// return Carbon\Carbon::now()->diff(new Carbon\Carbon($value))->y >= $minAge;
});
This way you can use the rule for any age you like:
$rules = ['dob' => 'olderThan']; // checks for 13 years as a default age
$rules = ['dob' => 'olderThan:15']; // checks for 15 years etc