Tall building with balcony and toddler?!

We'll be staying in a 65 story building with balconies in just a few weeks time. We originally booked it for the view and then found out that there's balconies in the apartments. We'll be staying for 7 nights for my daughter's 2nd birthday, and I'm a bit concerned about safety issues. I'm terrified that somehow she may open the balcony door and climb over the edge during our stay. Is there anything that I can do to prevent her from accessing the balcony?