Quiet time can be anything quiet...and that will compliment or work with your child.
it can be playing a Leapster, or reading, or just daydreaming, or watching a video, or doing puzzles or simply nothing and just lounging.
And the length of time should be do-able and age appropriate. BUT if he falls asleep because he is tired, then he should still be able to do that or allowed to.
Even in Kindergarten... they still have nap time, and these are 5 & 6 year olds.
For me, I don't make nor require my kids to just "stay" in their room as a "must." Main thing is that they are content and in "quiet" mode....but you also need to have a "wind-down" time... so that they can flow into it too. IF expecting quiet-time to be RIGHT after some active activity...then don't expect quiet-time to be immediately after that. A child would need to "segue" into it, and allowed to calm down, first.
Lots of times, a quiet-time also will make a child fall asleep. So if your child happens to fall asleep during "quiet time".... then what? What is the plan? Is it okay or not?
If your goal is to make your child sleep earlier at night... then you don't necessarily have to eliminate his naps, completely. Some days a kid still may need a nap. But you can still put him to bed at the same time as you usually do.
One thing that will not work with quiet time... is to make it highly rigid and controlled. Sure have a ROUTINE about it everyday, regularly... but meaning, I allow my kids to choose what they want to do, and allow them to naturally find their place to hang out. So that it is fun for them too... and rested/peaceful, ie: quiet. THEN during that time... I ALSO tell my kids that it is "quiet time" for Mommy TOO. And that is when I read my magazines that are piling up or do desk work that has to get done etc. Or I even get a 10-minute cat nap. Quiet things for me too.
But, my kids still nap. My 7 year old will nap about twice a week now at her age... and my 3 year old still naps every day in the afternoon. I don't force it. They get tired and will actually tell me they are. And they go to bed by 8-8:30 at night and are able to, even with their naps.
But for "quiet times".... what I do is what I rambled on about above.
MAIN thing is to do what will work with YOUR child.... without it having to be a "battle." Quiet-time should be a cool calm mellow time... not something the child will think of as "banishment" or with dread.
Good luck,
Susan