I say go for it. You'll quit paying interest for the next 15 months, which can help you save several hundred dollars. To pay off $6,000 in 15 months, you'll need to pay $400 every month on average, not just months in which nothing "unexpected" happens. I advise you to find ways to cut your budget a bit more so that unexpected expenses don't throw you off track for getting your debt paid off.
As to your current card, leaving the account open can help your credit score. Having more total credit available and an older existing account will both work in your favor. That said, don't use the higher combined credit limit as an excuse to charge more. You've realized how bad credit card debt can be, so don't fall into that trap again.