As far as I know...if you are working in Saudi and decided to go for a vacation or an emergency leave....and you have reached your country....there is no problem in going to Qatar. As long as the new company can provide you a visa and plane ticket, then you can come here in Qatar.
There are hundreds of people who are working there in KSA, found a good job in Qatar, took a vacation, went to their country of origin, then flew and worked in Qatar. Some of them came here directly from Saudi. No need for NOC or exit visa.