R.L.
When my daughter was about the same age as your daughter, my mom insisted on watching her over night so that my husband and I could go away for our anniversary. I was anxious too. I was worried that my daughter would be upset I wasn't there.
But there was no reason to worry. It was really like out of sight out of mind for my daughter. A little bruising for my mother ego, but it was good for my marriage. Chances are that you are worring more than your daughter will. Enjoy your evening out. Your daughter will be ok.