Boeing South Carolina’s first 787 Dreamliner is in the air on the way to Texas to be painted in the color scheme of Air India, a company spokeswoman announced this afternoon in an email.

The historic plane, which took flight for the first time a week ago, left Charleston International Airport at about 1:20 p.m. and will land in Fort Worth, Texas around 4:30 p.m. EDT, according to Candy Eslinger, the spokeswoman.

Follow the plane’s progress here. : After Boeing completes the profile flight, Leading Edge Aviation Services will paint the plane. Previous Air India liveries have been mostly white, featuring red lettering and a gold sun design on a red tail.

According to Eslinger, the plane will return to the Lowcountry early next month “to continue to be readied for delivery to our first customer by mid-2012.”

Meanwhile, Air India, which has contended with financial and labor strife for years, is reportedly refusing to take any of the 27 Dreamliners it has ordered until it works out with Boeing compensation for the three-year delay in the jet deliveries.