I wouldn't bring my own daughter as a toddler to the signature places, but I would have to Le Cellier (my son could always go to any restaurant).
Here is some advice:
1. Eat early, you have the best chance with an early ADR of not having to wait to get seated.
2. Know what you want before your waiter(ress) reaches the table. Look at the menus earlier in the day (they are posted outside the restuarant). Look at allearsnet (subject to change, but it will give you an idea).
3. Let you waiter know that your toddler isn't going to tolerate a long meal and anything they can do to move it along will help. Most will jump to the task of getting your food promptly. They should also warn you if you order anything time consuming to get.
4. Order all your courses at once. And consider just ordering dessert to go. It will be lovely on your balcony while your daughter goes to sleep!
5. Make sure to bring cherrios/goldfish/finger snack of your choice. My kids were never toy/crayon kids (until about two years later) but some parents have luck with that sort of thing.
6. Finally, don't expect a quiet leisurely meal (though some kids cooperate). Ours were usually exhausted enough by their day to behave well through a short meal.