Just stop and think for a minute.
If double beds could be made light, strong, durable and attractive for around £100, don't you think we'd all have one?
Most kit furniture (eg Ikea) is amazing value for money. It won't last forever, but the way you treat it and move it around will make a big difference to it's durability.
You could do it as you have sketched, but you won't be able to move it and it'll be a great waste of space, unless you design some storage into it.
You'd need 2x2 battens for all the joins, screwed, and preferably glued for strength.
The exposed cut edges would be very vunerable to damage.
And if your floor is in any way uneven, the whole thing will tend to twist/buckle. (So best to support it on four legs, a bit like.... a real bed.)