L.B.
I've grown-up in Texas with tornadic weather during Spring and Summer all my life. I remember as a child that on nights when there was a tornado watch or warning, the 3 of us kids would be placed in beds on the floor in the hallway of our home. It was the safest place in our 1-story home, away from glass windows and loose objects.
My dear friend's entire neighborhood block was hit by a tornado in Farmers Branch when I was in 2nd grade and many were injured and the homes were torn apart.
With all that said, now as an adult, I continue to be cautious during severe weather and especially like tonight with a tornado watch. I would definitely bring your child downstairs on these type of nights. I have a 3 year old whose bedroom is upstairs and our Master bedroom is down too. So, I'll be bringing her down tonight as well.
It's good to be cautious in severe weather or other types of disaster issues. Your instincts are good. Hope this reinforcement helps. Take care. Many Blessings - L.