A baby gate is a good idea, that deterred ours when they were little from all kinds of things and came in handy when our dog was just a puppy!!
If you wanted to hide it from view, you could have a piece of plywood cut the same size as the framing around the space. Then attach some really good velcro strips around it, so that it's harder for a toddler to pull off. The outer part could easily be disposed of when you're ready to move, and the velcro attached to the frame would come off and clean up with some Goo Gone.
We covered an entertainment center with clear plexiglass this way when our children were very little. It was easy to remove when they got older and understood they couldn't touch what was inside!
"And let us consider one another in order to stir up love and good works," Hebrews 10:24