I'll be very honest with you; in that trailer my concern would be her trying to go over the tailgate. I've seen it happen, and it's not pretty.
Most horses *do* ride better without a center divider so they can spread their legs for better balance, but I wouldn't risk it in this situation. If the center divider goes all the way to the floor, you can make a cut out at the bottom that will allow for that.
If that trailer is your only option, I would leave the center divider in to prevent her from trying to turn around. Or I'd wait til I could use a stock or a closed trailer.