Going by public documents, it seems like the intention was to have a separate organization pretty early on (although I can't say about the very beginning since I wasn't involved).
The Articles of Incorporation for CFAR (called Feynman Foundation at the time) are dated July 18, 2011, and 501(c)(3) status was approved on July 26, 2011.
MIRI's 2011 strategic plan (updated August 2011; unclear when it was first written) says "Encourage a new organization to begin rationality instruction similar to what Singularity Institute did in 2011 with Rationality Minicamp and Rationality Boot Camp."
The Minicamp took place in May–June 2011, and it seems like the Boot Camp took place in June–August 2011, so it looks like by the time the first workshop finished and the second was in progress, the plan was already to start the new organization. However, it's still possible that there was no plan for a separate organization before or during the first workshop.
MIRI's December 2011 progress report also talks about plans to create the "Rationality Org".
I also wrote a timeline of CFAR a while back, which has more links.