1,400 light years/~45,000mph (the speed of New Horizons) = 23,844,146.8 years of travel time. I guess that wouldn't be impossible, but if you've got a ship that can last that long in interstellar space, then what do you need a planet for? Or for that matter, a star?
You wouldn't try to make a 1400-ly trip, and you would try for a much faster departure than NH did.
There are about 10 stars we know about within 11-ly of earth. A serious attempt to reach one would involve doing slingshots around many bodies in the solar system, probably culminating with a dive to the Sun in order where the major rockets would be fired. (The Oberth effect says you get the most ∆v boost at the point closest to the orbiting body. You cannot logically use the Sun as a passive slingshot because you are trying to leave the solar system.) Getting the speed to 1% of c this way looks entirely reasonable, which gives about a century of travel time.
It would be very expensive, but in a few more centuries society will be a lot richer. This is also something that would only occur after significant colonization within the solar system, and mapping of distant star systems to find good candidate systems.
