How should I Puppy-Proof this balcony?

I will be moving into a new apartment (sublet) for at least the next few months with my 13 week old toy poodle.

Before delving into the issue at hand, here are some obligatory puppy pics:

Puppy on Couch

Puppy when super young

The apartment we’ll be living in has a double balcony, 2x21.5 feet long

Along the balcony there is a 4 inch gap that I am sure the puppy could fall through if she tried hard enough.

There are a bunch of photos of the problem here: http://min.us/mxz2US9tt

And a little video here: - YouTube in case anything is still not clear.

So what I’m looking for is something temporary I can either do myself (or more likely) ask a handyman to build for me to ensure the balcony is 100% safe for my puppy. What strategy, materials etc can be used to fix this problem?

If your landlord allows it, you could likely fix that yourself with a little chicken wire. Home Depot has a plastic version in a 3’x25’ roll for twenty bucks.