Hi M.,
My 13 month old has done the same for months now. He surprised himself once by throwing up, but I'm not quite sure he associated it with the gagging. It is an attention thing and at the same time, he starts it when he is teething. So I don't pay attention to it anymore, except to get him a dose of Tylenol in the next few minutes. I do try to distract him at times, but not in direct response to the gagging. He doesn't do it as often now. Believe it or not, some kids don't mind that sensation - it's learning a new response their body has - they have a limited amount of control over it. So that makes it interesting far above and beyond losing all the precious food (and the time it takes to ingest!) that they had for lunch (time and money really having no value except when needs aren't met NOW! :) and interesting, when left alone, is what a little boy looks for.
Try a toy from a different room (moving it into his line-of-sight, not brandishing it for him to notice) or a game with the 3 year old that the 1 year old can join in (like singing a song, or This little piggy, or old macdonald or Bingo or...)
Good Luck!
M.