This is a common thing with very young bunnies (and some older ones to)! I got my mini rex when she was approximately 4 months old, and what we had to do was block off small spaces that she could squeeze into, either with NIC grids or with something else to fill the space.
Our old entertainment center had a tiny 3 inch space along the bottom, just big enough for her to squeeze her little body under. We took a flat piece of cardboard and folded it a few times, and then tucked that into the opening. It didn’t look great, but it was a temporary solution for a couple months until she was too big to fit underneath anymore. You could do something similar for the sides of the dresser.
A new product that’s out now are those swivel sockets. They have 3 outlets on either side and allow you to have stuff plugged in to the side, this way you can move furniture closer to the wall, but still have stuff plugged in behind. Just another thought.