She's in a cot, in a grobag.
5.15 this morning. She's now yawning in front of Charlie and Lola.
Thinking we should get a gro clock and give it a go. She knows what stars and moons are, so she might possibly just get it, even though she's little.
seeker, you've said this before on another thread I was on. Sorry, but getting up at 5.15 isn't acceptable to me no matter what time I've gone to bed. I just cannot put up with it any more, waking at that time makes me miserable.
We did push her bedtime back gradually to 8.15, but the effect was negligible. Her nap is usually about 1.25 hours, but it varies. It's definitely too soon to cut her daytime sleep, isn't it?
I don't know about the bribe idea, the only thing she is doing 'wrong' IYSWIM is not lying silently in her cot until it's time for us to wake up. Not sure how we'd explain that one. 
Thank you for the ideas and sympathy. I'm so fed up of talking about bed times, nap times and sleep with an equally grumpy DP.