As per my experience, passport " HAS TO BE 06 MONTH VALID " for International travel.
My freind was not able to board a flight ( Her passport was 4 mnth valid )
 
Nepal embassy will issue temporary passport which will be valid for 01 yr  for which it cost $20.00. For more infos please call them or check their website.  It takes 2 days , not more than that.  After you receive the other passport you need to resend temporary one .., they will void it.

Its an International travel, don't take a risk. Carry both Old and new passport to avoid any cross question in immigration.
(We did the same thing)

Embassy will keep the copy for further process.


No hassle.


Good Luck !