I have this kind of 'rearcar', except here it is more like 'frontcar' and actually it is called milk cart.
This is just example photo from some Japanese site but what I have is almost the same minus the sides:
I did found photo from this site:
*istD Gallery
I'm thinking of putting trailer to my bicycle, but I don't know if I should use that cart as a base, weight might be bit on high side as it is made to easily carry 100kg or even more, so cart is very strong and bit of heavy, I guess it alone weights more than 20kg.
It would be simple to connect it to bicycle, last picture at bottom of this page shows how someone in Japan has connected 'rearcar' with rather simple means to bicycle:
Bicycle trailer - Wikipedia, the free encyclopedia
I can use some metal parts however as I have equipment to make things from metal, just source material is something that I'm lacking always.
My use for trailer is mostly to haul shopping bags, but also I'm interested if it would be possible to make fairing to cart so that it would help with aerodynamics, but for this my cart might be bit too wide.
I have some very thin walled metal pipes too, only issue with those is that they are really thin and very difficult to weld on.
Using cart would leave back of bicycle relatively free for putting some fairing there to improve aerodynamics, currently I'm loading bike bags to rear of bicycle but those are tad small to really put week worth of shoppings there, even it might even help a bit with aero.
Wind is my greatest nemesis with bicycling.
edit: I did quick hack job to attach cart to bicycle, took few horribly bad photos, that camera has broken screen so it is bit of luck to get shot right, lately it has also developed -2EV from somewhere and without seeing impossible to fix that.
Anyway, here is the cart, just the frame at the moment, leaking tires, one nut missing from wheel axle so one tire has variable toe:
Hinge is rather dirty job, somehow center did move after I drilled hole perfectly center of metal, riiight.
It works, of course needs lot of work to make usable, but even that it weights a lot it seem to follow nicely. Floor is made of wood and does weight close to 10kg alone, with that it is easily 30kg, so need to think way to loose weight from that.