A very interesting idea for a fantasy society, I can definitely see this as being fun to use in a RPG-type setting.

I do agree with the other posters here though, a 1 to 1 exchange for any and all goods just doesn't make sense in any logical scenario. Some goods have an inherently greater value based on primarily two factors:
1) Rarity (scarcity), materials that are useful but rare are inherently worth more.
2) Labor, materials and goods that require more effort to make or acquire are inherently worth more.

I'm sure others who are more schooled in economics could break that down into greater detail, but those two guidelines work pretty much all the time.

That is why, say, a tool made of wood and iron is worth more than the wood and iron it is made of, because it required labor. And that is why 20 lbs. of salt is worth more than 20 lbs. of loose rocks, salt is rarer (and requires more labor to obtain) than loose stones.

I would suggest that you can keep your non-currency society intact, but maybe mix it up a bit with some pseudo-currency standards, like the exchange rates mearrin69 suggested.

Think about your society. What are their most common goods? These could be used in place of the normal dollar/euro/gold type of value system.
"That little shack over on the hill? It'll cost ya ten hogs and seven chickens"

I'm reminded of the Bone comic book series, where in the little town of Barrelhaven the standard form of currency was the egg.