If you're not on the list of 30 countries which can purchase a visa on arrival at the Doha airport, I think the logical place to go would either be the Qatar Embassy/Consolate in Dubai (surely they have one), or to a visa company/travel agent for assistance/referral.

If you're planning on coming the 25th, you might want to get hopping. As you're well aware, Eid is upon us, and I don't know how it is with the UAE, but the Qatari government will take a whole week off. This means your stuff will sit on the desk.

Just a bit of advice.