Leaving aside the vagaries of dot sights, which I'm not sure are really that relevant to IDPA anyhow, I've got a couple of thoughts on the original subject,
First, I think that unless you're already a highly skilled shooter, it might be better to shoot your matches and do most of your practice with a full size gun. It's easier to learn when you're not having to fight with your equipment. Much of what you learn running a full size gun will transfer to the little one, especially if they're the same platform. I think that shooting and practicing with only the little one will definitely slow, and possible limit your growth as a shooter.
A couple of matches with the little gun may be quite valuable. Matches are fantastic at exposing flaws in equipment, technique, and expectations. I just think that in this case, enough is as good as a feast.