I don't think it's a good idea to exactly mirror the insurgency, but I'm hard pressed to think of the counter insurgent movement that succeeded without adopting at least some of the tactics of its opponents. E.g. the US Cavalry picking up Indian scouts for help with tracking, lightening some combat loads, etc. in order to keep up with fast moving Indian opponents.

That said, the Iraqi Army has some advantages the insurgents never will, and they'd be fools to ignore them: funding to pay recruits, training in small arms and tactics from US soldiers, access to sophisticated electronic and aerial intelligence, a certain degree of air and armored support, etc.

What, specifically, should the Iraqi army (and perhaps the US army) attempt to copy from the insurgents? I'll throw out a few ideas, perhaps some people here can come up with others.

1) Camouflage. The insurgents virtually never reveal themselves until they strike. Select Iraqi soldiers should definitely be out and about in their patrol areas in plainclothes or unmarked civilian vehicles. Sufficient issue of concealed weapons would be a good idea. A better idea would be meticulous record keeping and debriefs to make sure these soldiers aren't sidelining as death squads or criminals. Perhaps digital cameras or GPS devices could be issued to provide some evidence of that.

2) The rumor mill. Iraqi society receives much of its information by word of mouth. Simply being aware of the latest urban legends could be a great asset, even if you don't debunk them or start your own.

3) Internet age communications. The insurgents make a big deal out of their websites and so forth. Individual units, officers and soldiers with their own blogs, sites and so forth could start to counteract the other side's dominance in the Information War.