Well, it might happen -- at least, it's in the realm of possibility.
The site Hypable posits that Rowling might be among the “well-known children’s authors” to write a short "estory" in celebration of the Doctor's 50th anniversary this year. This supposition is based on a recent press release from the BBC announcing the project:
"A new series of Doctor Who stories is set to be published monthly to celebrate the 50th anniversary year of the hit television programme.
The 11 tales, known as "eshorts", will each be written by a well-known children's author.
Each story will feature one of the various regenerations of the Doctor, starting with William Hartnell, who played the character from 1963-1966."
The publisher of the stories refers to the authors as a "who's who of children's fiction" -- what such list wouldn't include Rowling?
Right now this is all fannish speculation -- but the BBC will announce the first author on its Worldwide Doctor Who Facebook page on January 7, with the first story to go online on the 23rd of that month.