At this age, you could get her the Crayola Color Wonder markers or the fingerpaints. It makes the colors appear, but if she colors on a table cloth, no worry. I introduced these at about 14 mos. with my oldest when we were invited to a very nice restaurant, out of town where we did not have anyone to watch her while we went. And those only came out for quiet occasions, so it was a real treat for her.
Like the others have said, she is too little to be expected to sit still, if she acts up, out of politeness to others in attendance, take her out for a few minutes. As for the luncheon, ask that her food is brought out immediately. This allows you to feed her, and hopefully by the time yours comes, she is still in good spirits and you can enjoy yours.
My husband and I used to ask that our kids food be brought right away along with one of our meals and to hold off about 10 min. for the other. One would eat, one would cut up the kids food, feed them, and by the time the second entree arrived the first parent was about about done and able to take over, so we'd both get a hot meal. It's what worked for us, thankfully it is better now! Good luck!