For us, nap time didn't get shorter...but bed time got later and later. She used to take 1.5 hour naps and then would usually go down no problems at 7:30-8 pm. Over the course of a few weeks I noticed that she wouldn't fall asleep until 9-9:30 (just layed in bed and talked to self, etc.).
So one day I decided to forgo the nap and was surprised that she wasn't super crabby like she was in the past.
It is a transition tho...somedays she is crabby and needs that nap...then I just bump bed back a half hour or read a few extra books, etc. I've tried letting her nap for only 30 mins or so...but that seemed to result in a cranky pants who had a hard time waking up from nap. Once in a while she's a little crabby at night...but then we just bump bedtime up a half hour...but it's not as bad as you might think it will be.
For quiet time, I put on a tv show of her choice and have her lay down with blanket and pillow (either on couch or in her room). If she gets up, I just put her back until the show is over.
Since no naps...I've noticed she doesn't rely on me as much to tell her when she's tired. She's seems to have learned that it's OK to sleep when tired...even if mom didn't go thru the whole bedtime routine first. If she needs to rest, she'll go sit down (and this active little girl rarely rests long lol). And in the morning, she used to jump up when her brother was awake...now if she's still tired, she'll pull the covers over her head and go back to bed lol.
For my daycare kids...until age 3 they have to lie in bed for at least 45 min...if they don't fall asleep that's fine...but they have to lay there (can have radio if they want)...unless parents wish otherwise...most of the time they fall asleep within 15 min. However, alot of the 'working' parents like to have their kids up later with them since they don't see them during the day.
Wow...that was a longer response than I thought it would be...I'll stop there lol