Can I use "Idż kupować piwo"?
It's quite strange. Buying beer should be a rather quick action, and here you put it more like "Go and be in the process of buying beer". It's hard to imagine hearing that.
In fact the most common and natural thing to say is "Idź po piwo". There is no information about where the person should get the beer from (a shop or a fridge) but usually it's clear from the context.
Also, it's "idź" not "idż". Big difference.
I'm surprised that it wasn't accepted so far... added now. Even if it technically doesn't mention buying, I agree that it's just very common.