Hi, I think 18" is a bit higher than a standard petshop rabbit cage but imo too low if he spends most of time in there, it is suggested that they should have room to fully stand in there without touching the roof, here's a guide to rabbit housing with all recommended sizes
http://www.therabbithouse.com/guide_size.asp
Also some good read about housing here, and check out their link to x-pen living there's some ideas too
https://rabbit.org/faq-housing/
But I love the idea because it would be really space-saving for you and a plenty of room for him to hide, rabbits love underbeds too. I am myself also very limited and got a loft bed it is 2 m (78") high and I also have a large desk there which is about 70 cm (28") high so it's quite spacious. This bed in this link but mine is white
https://www.ikea.com/gb/en/p/svaerta-loft-bed-frame-with-desk-top-silver-colour-s59151271/
For your frame if I had it I would attach a large dog crate to it, just by the wall they are high enough, only the trays are not high enough so if your rabbit is a digger you have it all around the crate on your floor. But this is fixable for sure.
Like this residence is 107 x 70 x 79 cm and you can put a desktop on top and use as a large night table or for many more uses actually
https://www.amazon.com/Savic-Residence-Hammer-Tone-Crate/dp/B07KSQVBY5
So he'd have full run under your bed and a higher crate to stand up, my rabbits love dog crates and you can remove walls to join two middle-sized together so I have 2 x 80cm x 60 cm x 60 cm high joined together like a tunnel 160 x 60 x 60 cm or side by side 80 x 120 x 60 cm, also you can remove bottom grids and make a wooden base covered with lino, you can use removed walls to extend them even more (60 or 80 cm extra in length). I like medium size because of extra large crates are too high about 80 cm and medium size is about 60 cm so fits under a standard table safes space.
