I agree Kabayan dont call the embassy as they are not going to entertain calls especially regarding procedure or what so ever.

I was a direct hire myself so if you are also a direct hire hope the steps will help you.

1.) You need the contract from the new company.
2.) Go for medical examination as Medical Exam Results is a requirement from the Qatar Embassy.
3.) Go to the nearest DHL branch in your place and send your documents (contract,passport,medical results) im not sure if they will also require you an authenticated NBI clearance coz they require me an NBI clearance during my time last Dec 2010.

4.) After 5 to 7 working days your documents will be returned to you also via DHL, its advisable to follow up your documents to DHL as they wont even try to contact you even if they have your documents early than the prescribe period.

5.) You can now proceed to POEA to process your work/travel documents. Please make sure that the Position or designation on your contract will fall under the professional/skilled category coz you wont need a POLO Authenticated Contract. Category 2 workers or what they call non-professional/non skilled workers need to have their contract authenticated by the POLO or consulate office here in Qatar (i.e. clerical jobs). If you are under Category 1 or the professional/skilled worker then you can proceed with the processing of your papers in order for you to travel.

6.) Sometimes, depending on what are the terms on your contract the POEA assessing your contract might asks you to ask the company that you'll be joining that they will only terminate you on certain conditions or something like that...its a letter from the company that you need to give the POEA.

7.)After all the documents are verified and accepted by POEA and payment of certain amount (less than 7000pesos) you can take your PDOS.

8.) After POEA you can travel to your country of destination (Qatar).

9.) Make sure that you have your OEC (receipt from POEA) as it is the primary document that the immigration officers at the NAIA is looking for.

Goodluck, I hope it helps.