Translation:We want to go shopping.
You are right that shopping is more closely “购物”. 买东西 is more generally "to buy things", which also can mean shopping. However, if this Chinese sentence is used, as it can be, to catch the attention of a shopkeeper or salesperson that a customer is here waiting, the English translation wouldn't work.
Ok, I generally know what this sentence means, but as usually on duolingo, there is the question what is accepted translation. When I hover on 买东西 it says "shopping", so IMHO the best translation would be "We would like to do the shopping". Well, of course that's incorrect. The correct one is "We would like to buy things" - which is obvious or "We want to GO shopping" which isn't that obvious as the original sentence lacks '去'.
No Go...Where is the Verb - to go? (We want to buy things. or We want to shop.)