I agree, I can't stand whining and I know it means tiredness. It's just odd, she used to do 2-3 hours usually spread over 2 naps not long ago but she dropped her afternoon one (just plain wouldn't sleep).
I try to stick to making her go down but she stands and sings and then eventually starts crying and after an hour I just get her up. And then she might still rub her eyes or look tired.
She does pretty well at night, although she used to sleep through, her teeth get her up every few nights.
I suppose the bright side is that she wakes up later when she's been like this.
My DD dropped daytime naps totally at around 12 - 13 months. She'd been cycling down since about 10 months, so it went from daily, then she'd miss 1 day a week, the 2, etc, until she was only napping when she was ill or on car journeys (rare as we don't have a car). She sleeps well at night (albeit a nightmare to persuade her to go to sleep) but seems to need less sleep than others her age. At 1 year she used to sleep about 9.30-8, at 4.6 years she sleeps about 8-6.
All kids are different, as long as your child is healthy, alert in between sleeps, & you are managing reasonably well with whatever routine you have, it's fine.