So free trade, but no money? Ummm, okay...
Money is the necessary conclusion to free trade. Otherwise I'm going to be sitting here with my 16 chickens waiting and hoping that a purchaser who happens to need what I have right now and also happens to have the things I need to trade for will come along. It's incredibly inefficient and can be flat out wasteful with perishables that you've just made it much tougher to exchange for what you need. Seriously, do you realize how much that would limit free trade? Well, actually it won't, because traders won't let it if they have a more efficient way.
Money was created as a medium for exactly that reason. You know what would happen if you eliminated money? People would find something else that has accepted value to everyone and trade with that instead. End result, you guessed it, money. You cannot simply eliminate money. The market (no not like a stock market, I mean your traders in your scenario) would always opt for this over bartering. It's far more efficient and the necessary conclusion to free trade.
Now that the economics 101 lesson has concluded, maybe we should discuss some PoliSci101, because communism/socialism (or whatever variant you subscribe to) does not work on a large scale for the simple reason that it lacks the proper motivation, when resources are shared and there is no incentive to give more than you take, and little incentive to innovate or do more than you have to.
On a small scale, sure. There are plenty of small rural towns where a communal attitude still exists to some degree, but this isn't antithetical to capitalism, making (trading) the equal amount of what you produce for society.
So this is where I'm confused. If you have trade/bartering (and thus money), that sounds a hell of a lot like anarcho capitalism, even if there is a communal attitude (In fact I don't think anarcho-capitalism is possible either on a large scale without a paradigm shift away from things our consumerist and greedy priorities, and towards more cooperative and advancing ones).
Anarcho-capitalism would not negate the possibility of communal socialism (on a small scale, the only way it works), but your system isn't getting rid of free market capitalism either. Where there is trade, capitalism exists. It is not a dirty word once you remove the "crony" out of capitalism and replace it with free.
Aside from that, I'll probably exit this conversation now, as the way that I've heard anarco-capitalism could actually work, it sounds an awful lot like minarchism. I think we can all agree (aside from maybe our socialist friend here) that the more localized and accountable, the better it's going to work.