Yes, you can.
It is a case explicitly stated in the Ironwood spell's text.
[...] Using this spell with wood shape or a wood-related Craft check, you can fashion wooden items that function as steel items. Thus, wooden plate armor and wooden swords can be created that are as durable as their normal steel counterparts. These items are freely usable by druids. [...]
So a relevant skill check is required. The most relevant skill among those listed in the manual is Craft (armor). Being the list of craft skills not exhaustive, I think that Craft (woodcarving), Craft (woodchanting) or other wood related skill could be reasonable.
The check - as per the Craft (armor) skill (see table) - has a DC = 10 + AC bonus. That is: 16 for a breastplate.
However, as already stated by Rhylok, Ironwood has a limited duration. So, if you're going to make a magic wood armor (with a bonus higher than the enhancement +1 bonus the spell itself provides), you should cast it over and over. Sadly, the spell is not listed among the ones naively susceptible to Permanency, but you could ask your GM. With his/her allowance, it would cost 15'000 gp to be rendered everlasting, and will require a Sorcerer or Wizard with a minimum caster level of 14.