I played in my first junior golf competition when I was 4. Me and Dad have found that there are opportunities to get involved in competitions but to begin with they are hard to find.
I think it is better if you can play against players of your same age, if you are lucky you may find a local club which does run golf events for younger children but usually they don't seem to start to around age 10.
Some exceptions to these are the US Kids Tournaments, National Skills Challenge and the best (in my opinion) the British Junior Golf Tour.
I love competing, of course I don't always win or even finish high up, but I get to meet other golfers of my age and it helps me to know what I need to get better at.
Here are links to the websites for the competitions mentioned above.