Validity of Passport for less than 6 months , will a visa be issued?

My daughter would like to accompany her school trip to Beijing for a Model UN conference . She is 14 and a US citizen . We are presently living in Tokyo with a long term residency visa for Japan. Her passport expires June 30th 2015 and the trip is 15-19 th of January 2015 . She is shy by a few days on the passport validity of 6 months for obtaining one.