Running
nohup php artisan queue:work --daemon &
Will prevent the command exiting when you log out.
The trailing ampersand (&) causes process start in the background, so you can continue to use the shell and do not have to wait until the script is finished.
See nohup
nohup – run a command immune to hangups, with output to a non-tty
This will output information to a file entitled nohup.out in the directory where you run the command. If you have no interest in the output you can redirect stdout and stderr to /dev/null, or similarly you could output it into your normal laravel log. For example
nohup php artisan queue:work --daemon > /dev/null 2>&1 &
nohup php artisan queue:work --daemon >> app/storage/logs/laravel.log &
But you should also use something like Supervisord to ensure that the service remains running and is restarted after crashes/failures.
Use >> to append to laravel.log. Using a single > will replace the file each time.