The Afghan embassy in Doha is very welcoming.
It takes 24 hours to process a 14 days visa. Visas can be in extended in 14 day increments once inside Afghanistan if you need longer.

The easiest flight from Dubai is on Safi Airways (you don't have to change terminals in Dubai) or arrive in Dubai and transit to Terminal 2 and take Kam Air.

Good luck.

QATAR
Embassy of Afghanistan in Doha
Tel: (+974-4) 930821-2 - Fax: (+974-4) 930819
Email: [email protected]
Ambassador: H.E. Mr. Khaled Ahmad Zekria

http://www.safiairways.aero/

http://www.flykamairline.com/

p.s. Wrap up warm at this time of year. Kabul is 1800m above sea lever and freezing cold.