Without sounding as a Parelli basher, I would say to take it very easy on your "games" work with the baby. You can really wear a horse out with them, and sour them to the whole thing with too much of this sort of thing . Pat himself says that the 7 games are just for a short period of time to get you to move on to things more directly related to riding, and he does not encourage people to stay a long time in this phase. STarting it now will have the possiblity of eventually kind of dulling your horse to them, I fear.
In many places where horsemanship is an ancient art horses are allowed to be horses until they are at least 2, handled for a few months, then put back out to just be young and then brought back in for real training when they are more like 3. So., if in doubt, give your horse time to be a baby. It'll pay off in the end, I think.