My baby and I will be sharing a room. I am wondering if anyone has any recommendations or ideas on how I can baby proof the handles on a dresser's drawers (please see picture); I'm worried about my baby falling and bumping her head on them.

And also an Ikea cube unit (Ikea website pic below). For the cube unit I was thinking of buying 13" boxes that fit the unit. But how do I keep baby from pulling them out? I've looked online but haven't found the right thing.

Thank you so much!