My eight year old really wanting to start playing tournaments this summer and I was okay with it as long it was not all about winning or losing, but making steady improvement in her game. She agreed and has kept to her word.
I would say let her play. Please make sure to hold her accountable for whatever goals you have her playing tournaments (fun, work hard, etc..).
Have Fun... some of the best memories of my life our during the car rides and lunches with my daughter during these tournaments