No! Waste of time. Focus on school and extra curricular activities so that you can get into a good college and/or start up a company. You have your entire life to date. At 13 it will only be a distraction.
I actually started dating when I was 12. I know it sounds young, but we have known each other our whole life. I am still in that relationship, And we are going strong I think that if it is okay with both parents, It should be fine! It should be encouraged! I dont think that any real harm can be done at that age, if any thing else you learn some about relationships <3