Arguably the best hope of understanding the tail end of the re-ionization of the intergalactic medium (IGM) at redshift z>6 is through the detection and characterization of the Gunn-Peterson damping wing absorption of the IGM in bright quasar spectra. However, the use of quasar spectra to measure the IGM damping wing requires a model of the quasar's intrinsic Lyman{alpha} emission line. Here we quantify the uncertainties in the intrinsic line shapes, and how those uncertainties affect the determination of the IGM neutral fraction. We have assembled a catalogue of high-resolution Hubble Space Telescope spectra of the emission lines of unobscured low-redshift quasars, and have characterized the variance in the shapes of their lines. We then add simulated absorption from the high-redshift IGM to these quasar spectra in order to determine the corresponding uncertainties in re-ionization constraints using current and future samples of z>6 quasar spectra. We find that, if the redshift of the Lyman{alpha} emission line is presumed to coincide with the systemic redshift determined from metal lines, the inferred IGM neutral fraction is systematically biased to low values due to a systematic blueshift of the Lyman{alpha} line relative to the metal lines.