If you restring a right hander to turn it into a left, you also need to rotate the nut. This is the bridge on the head of the guitar, otherwise the high e, and b strings will be loose and the e, a and d strings won't bed properly. Removing the nut is generally easy.
Sometimes the bridge needs changing too. Converting an acoustic guitar is an easy enough job for a guitar tech, so I'd suggest you find a decent guitar shop who can sell you an inexpensive guitar and then have their tech convert it as part of the setup process.