I agree with PDQBach. Simply getting PMP certified does not make you qualified to lead/manage any project. You have expertise in the construction industry. You understand risk and risk management in that industry (weather, equipment failures, labor issues, subcontracting, etc). The risks and risk management on other projects is not the same. And risk management is alot of what we do. As he also said, learning the lingo, laws and regulations, quality standards, etc are all different across the industries.
And to further reinforce PDWBach's point, the certification should be considered an add-on bonus or differentiator between two otherwise qualfied candidates. I'd hire an experienced IT Project Manager without credentials before a Construction PM with credentials, all other things being equal.
You might want to check out the sister site, geared to Engineering. You might find some interesting job opportunities or descriptions which are closer to Construction in terms of risks, resources, etc.
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The trouble with doing something right the first time is that nobody appreciates how difficult it was - Steven Wright