We report measurements of mesoscopic fluctuations of Coulomb blockade peaks in a shapedeformable GaAs quantum dot. Distributions of peak heights agree with predicted universal functions for both zero and nonzero magnetic fields. Parametric fluctuations of peak height and position, measured using a two-dimensional sweep over gate voltage and magnetic field, yield autocorrelations of height fluctuations consistent with a predicted Lorentzian-squared form for the unitary ensemble. We discuss the dependence of the correlation field on temperature and coupling to the leads as the dot is opened.