In fact, as of a couple weeks ago, most of the action at PI doesn't happen after 7, all of it does. They've roped it off during the day, which is too bad because it was fun to tour it in anticipation!
I've seen children your kid's age in PI before. There's little to do there, although I've seen parents in the Adventurer's Club with small kids and the CM's are really good with kids.
Opening up a discussion on whether children should be in PI usually results in strong disagreements. Personally, I think kids in PI are fine if you understand what you're walking into (others will strongly disagree). Know that there is drinking. With the exception of the AC and the Comedy Warehouse, all the clubs are basically dance clubs, very adult oriented. And the CW isn't really humor children would understand, although they keep it prettty clean. And in my experience, somewhere between 9 and 11 PM, the state of people drinking becomes more obvious. Just know that before you enter those pearly gates.
However, as wisconsinmousermom mentioned in her post, Downtown Disney is made for kids. There's so much to do there for kids, plenty of eating opportunities (and plenty of cocktails for adults who want one but don't want to expose their children to the bar district), and it has the added advantage of being free entry (PI is about twenty bucks a head cover charge, or a plus).
Hope that helps!
Pat