Generally speaking they recommend that you don't advance a child much if at all for math competitions, just because the kids doing these aren't randomly selected representatives of the average for those grades -- they're predominantly the kids who are similarly advanced in math. So kids doing high school competitions are almost certainly past Algebra 1, and may be long past. My Mathcounts kids are all 8th graders (except DS) and they've all finished Algebra 1 already (including DS). I have three Geometry kids, one Precalculus and one Calculus.
That said, there are frequently very specific rules about who is and isn't eligible, based on age/ grade/ etc. and within those rules you're free to do what you see fit. We actually did skip DS up, but we did it for the science fair (where it was becoming ridiculous to keep him with agemates) and according to the MathCounts rules a sixth grader is a sixth grader is a sixth grader -- it would have been really questionable to keep him back for that, while simultaneously moving him up for other things. Would he do better with another year of maturity? Definitely. But we decided it was worth the risk.
Actually most competitions are open to any grades "up to __" -- like the AMC-8 and the AMC-10. There's no lower limit and no eligibility limit, so you can register as a 4th grader but participate just as fully as an 8th or 10th grader. I would probably start with that, so as not to make any permanent decisions before they're absolutely necessary. Really I think the only one that's terribly picky about it is Mathcounts... and once you've tried some of the others you'll have a better idea of how you should approach that one.
