2yo exhausted by 9/10am?

[BookTart]

DD is nearly 2 and a half. She sleeps well at night, from 7pm - 6am, and only cries for us when she is ill. Daytime sleep has always been more of a problem, and recently she has begun to have the odd day when she skips her nap completely. On the days that she does sleep, it is always in the car on our way to or from somewhere, and it generally lasts 45 minutes.

In the last couple of weeks she has clearly been very tired by around 9 or 10am (rubbing her eyes, laying on the sofa etc.). I'm a bit confused by this, as she sleeps such a decent chunk at night. This morning she was so ratty that I took her out in the car at 9.45 and she was asleep within 5 minutes. I'm wary of doing this regularly as I know that too much sleep early in the day can lead to earlier morning wakings (and I don't want any earlier than 6!) I just wondered if this is a standard thing, and if it is how everyone else deals with it?