Qatar is not a member of the Hague convention and hence the apostille isn't recognized here. You'll need the chain authentication (Embassy Legalization).

1) Get diploma attested from your university notary

2) Get it attested from the county clerk.
3) Next from the state secretary
4) Next from the department of authentications - Secretary of State.
5) Next from Qatar embassy at DC
6) Finally from Ministry of foreign affairs in Doha.

Check authxperts.com. They are reasonably priced and get the job done. I got mine done through them. They'll do right from step 1 to 5. There are other agencies that do the attestation process .. just google it.