I'm 19+ 3 today and my mom started planning last week, the shower will be held in June. I don't think theres a 'right' or a 'wrong' time to do it, but you don't want to do it too early because you never know what's going to happen.
My bff and I started 2 weeks ago. I'm 24 weeks. Due July 10 and having it June 1st. That way if my other side of the family want to plan one. They can with flexibility and if we don't get everything we need, we have time to get it and everything washed.
My SIL told me to plan mine 3 months before my due date, all of my friends had it a month before theirs, but I also don't have any family of my own to help me out and she said it'd be better to have what I get from the shower and extra time to buy everything else that I need. :)