Yes you can legally own it. Yes, you can openly carry it. You can keep it on your side, in the open, or in any enclosed factory installed storage compartment (meaning the glove box, console, etc.); check out KRS 527.020 for more information on car carry at http://lrc.ky.gov/krs/titles.htm . You can also look at the thread at the top of the KY forum titled "KY gun laws."
EDIT: Scroll down to chapter "527: offenses realting to firearms and weapons" on the website I gave you and click the blue link; on the new page click on ".020 Carrying concealed deadly weapon." You can also go to chapter 237 for more firearm statutes.