I love loft beds. My husband and I had a queen size one when we lived in a smaller San Francisco apartment, and we had our office underneath it. Allowed for so much more room.
It always worried me though that all of our computers and stuff could be crushed it the bed fell somehow. So Steve got more wood to make it more stable (like how you have the one vertical leg, we had one on each corner and then we also secured the legs and the bed to some studs in the wall. Over time though, after years, things slowly become a little less stable (of course, we are two grown adults and so our weight is alot more than yours), and so we would have to maintain its stability about a few times a year by checking the screws and bolts and fastening them in tighter when we spotted any looseness. We made it so that bed would not move at all. If it did, we checked the wood and the hardware.
Your dad seem pretty darn handy and so hopefully he secured it well, (it just concerns me there is only one leg even if the bed is fastened to the wall. so if you have any doubts, as I know you wouldn’t want it to fall down on your bunnies, you might talk to him about it.