I like option 1. Definitely don't do the overnight layover, and I agree with Eclipse... get there as fast as possible. Having a tired toddler leaving airport, getting on shuttle, checking into hotel won't be so easy, and then you have to go back through security and sit at the airport, etc.

Leaving during the day means you're daughter will be awake for the first half of the flight and probably sleep a few hours. There's a lot of distraction/excitement on planes for young children, so if you take Option 2 with the late flight she might not sleep and be overly tired/grumpy. Plus you will DEFINITELY be more tired since you say you don't sleep on planes.