Option 2. And I'd do it like this.

Leave for the airport after dinner (so around 7pm, I guess, depending on when you have dinner?). Check in and go through security. Go to the bathrooms and get your kiddo changed into pajamas. Find a quiet spot near your gate, and set her up with some blankets and some sort of quiet activity like reading a book or watching a movie. Let her go to sleep at her normal time (or if it were my kid, a few hours after, since the airport is more exciting than bed!)

When your flight boards, get on as late as possible. Wake up your kid, try to get to your seat with the minimum of fuss, hope she falls asleep reasonably quickly. See if you can then both crash out and get 5-7 hours more sleep.