Google says they penalize you if you have multiple domains with the same content, but I don't believe they really do yet.
We have a number of sites with both .com and also local domains (.ca, .au, .uk, etc.) and have not noticed any problems yet. We SEO all of these sites and monitor them closely, and all are performing well.
P.S. You could also do a 301 redirect from the old site to the new site. This is what Google advises is the proper way to transition to a new domain name and is probably the best way to handle it, if you plan to faze out the old domain eventually.
Cornerstone Technologies
www.cstech.net.au