The Software Update Icon does not exist in my System Preferences dashboard

The model year of a MacBook Air is available at Apple menu > About This Mac.

A mid 2009 MacBook Air can be upgraded to El Capitan 10.11.6 but no later version. See: How to get old versions of macOS - Apple Support

A late 2010 through mid 2011 MacBook Air can be upgraded to High Sierra 10.13.6 but no later version. See: How to get old versions of macOS - Apple Support

A mid 2012 MacBook Air can be upgraded to Catalina 10.15.7 but no later. See: How to get old versions of macOS - Apple Support

A mid 2013 and early 2014 can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to get old versions of macOS - Apple Support

An early 2015 or later can be upgraded to the current version of Monterey macOS 12. See: How to upgrade to macOS Monterey - Apple Support

If merely looking for updates to current OS. Go to the Apple in the top left corner. Click on it and then the App Store. Once there click on Updates in the menu.