Thanks Henry. I forgot to mention that you can apply, say, some clear shipping/packing type tape to at least the lower edge of the plexiglass so it doesn't scratch your balusters. I used a fine wood file to 'smooth' out the other 3 edges so the kid doesn't hurt themselves when the plastic is grabbed. Also, use the same file to round-out the edges somewhat too. The bigger the radius, the less likely you run the risk of an inadvertent 'poke'. If possible, try to put the drilled holes NEAR the corners (at least) but NOT tooooo near. This way, the corners can't be pulled out that easily. And use a pair of wire snips to snip off the excess wire tie after you've installed it through the holes and around the baluster.
ANd good luck with the Safety Gate. If you're interested in being REAL conscious about safety, go ahead and get on your hands and knees and crawl around to see what you can get into. Don't forget to reach for things assuming the kid can pull himself/herself up. Especially things like TVs on stands or on sliding shelves in entertainment centers, floor lamps, small objects, chairs, etc., etc.. Kids like to use 'things' to pull themselves up on. Try to envision what could happen if they hugged the Teletubbies on TV where the TV was on a sliding shelf. (It could end up on top of them.)
There are lots of sites on the WEB that talk about Child Safety. Use key words like 'child', 'safety', 'stairs', 'doors', etc., etc., and you'll get LOTS of hits on your search. If you need more on this, do ask. My best to ya and hope this helps.
PS: The plexiglass idea came to me when I wanted to try and put something up that wasn't too conspicious. There are 'meshes' made for this but you can't custom-fit them all the time. Plus, I don't mind doing the work anyway.