Kabayan,

Do not call the embassy of Qatar in Philippines.

1. If you are direct hire (your new company don't have agency in the philippines you can start the processing in POEA provide the following contract of the new company and the will guide you for the rest requirements)
2. Proceed to the nearest DHL office in your place.
3. DHL will process your visa stamp (Single entry visa will be stamp to your passport, approximately 3-5 working days only to process)
4. As soon you received the passport with visa stamp you can start processing again in the POEA office. PDOS, OWWA, Pag-Ibig etc.
5. After all the formalities you can now proceed to leave philippines