FFT peak estimation: Zero-padding vs signal repetitioon
If you repeat your data, you will have discontinuities where the sequence ends meet.  These will cause spurious peaks in your spectrum.  You could apply a window to the data to taper it at the edges, but that would be a fair amount of work, and you'd need to work out a window that doesn't color your spectrum.

I would just go with zero padding.  It will mess with the amplitude, but that should be fairly easy to deal with (scale by constant factor after FFT.)