Do I need to update Safari 11.1? Thanks

If you can't upgrade to Catalina, see if you can upgrade to an earlier macOS version.

How to upgrade to macOS Mojave - Apple Support

How to get macOS High Sierra   

Check to make sure your applications are compatible.

Application Compatibility

Also check to make sure there is a compatible driver for your printer.

Do a backup before installing, preferable 2 backups on 2 different drives.

Please read How to update the software on your Mac - Apple Support.

Learn how to upgrade to the latest version of macOS

Learn how to upgrade to the latest version of macOS describes how to obtain the latest macOS version, which incorporates the latest Safari version.