Please explain how you've reached your answer. I know what my answer is, but I was wondering what others think about it.
In The Lord of the Rings: The Fellowship of the Ring (extended edition) we have Bilbo record the date of his eleventy-first birthday as the 22nd of September, 1400 (Shire Reckoning; year 3000 of the Third Age).
In the Director and Writers audio commentary for LotR:FotR, Peter Jackson and Fran Walsh explain how they further altered the timeline of the story. This helps to explain some of the discrepencies between the book and films such as Sam, Merry and Pippin appearing at Bilbo's birthday party as young adults.
JACKSON: This is actually a case where we changed the timeline in the book. I think, from memory, 17 years goes past in the book from the time when Gandalf leaves to find out about the Ring to the time that he arrives back in Hobbiton to warn Frodo that this is Sauron's Ring; and in our movie we felt that this was just too long a time so we reduced it to seeming like a few months had gone by.
WALSH: Well, for those who know the book, you know there are fairly leisurely time-frames in The Fellowship of the Ring, and this was not a luxury that we could indulge in in the making of the film. We had to compress the timeframe in order to get the film underway.
JACKSON: And I like the idea that Gandalf had been sleeping in, under ditches and hedgerows, and had this sort of tramp-like existence trying to get himself right across Middle-earth on this sort of six or seven week journey to rush back to Bag End. So that's why had Gandalf looking so disheveled.
It is obviously impossible for Gandalf to have left Bag End on September 22, researched the Ring in Minas Tirith, interrogated Gollum and returned to Hobbiton in time for Frodo to leave the Shire and reach the Ford of Bruinen by October 20 of that same year. That gives us an earliest date of departure for Frodo and Sam of September 3001.