When: December 2011 - April 2012
There were reports of a hookup in New York in December 2011, but it wasn't until April 2012 that we got photographic evidence of the two being boyfriend-girlfriend in public. Some reports even had Joe moving a pile of stuff (hers, by implication) into his apartment.
Smash probability: The purity ring is at the bottom of a lake in Middle Earth at this point, and she's a hot model (who may or may not have taken permanent residence in his home/bed). Really, who wouldn't?