Good question about how long Tom was in Vegas. My guess is not too long. For whatever reason I think the discussion in the den where Michael said he was making Carlo his number one man in Vegas, and
told Tom he was "out" was probaly in Febrary-March.

Vito dies in the summer of that year, so my guess Tom went to Vegas right away, set up shop, drew the contracts for Johnny Fontaine, and gathered enough information to inform Mike that Moe Green was losing money, that his hotel was vulnerable, and that he slapped Fredo around.