Benefiting from the time-frequency analysis and multi-resolution characteristics of wavelet transform, wavelet transform profilometry（WTP）can accurately extract the phase map carrying the height information of the measured surface from a single frame of fringe pattern. The difficulty and accuracy of phase demodulation in wavelet transform profilometry depend on the choice of wavelet. Complex wavelets can be directly used for fringe phase demodulation. The nth-order derivatives of the one-dimensional Gaussian function satisfy the admissibility condition of wavelets, and the spectral distribution of each side-band exhibits smooth and asymmetric characteristics. These 1D functions, as 1D real wavelet bases, combined with the 2D complex wavelet framework, can be used to construct two-dimensional complex wavelets with good directionality and smoothness, suitable for fringe analysis, effectively improving the accuracy of phase calculation in wavelet transform profilometry. The spatial-frequency characteristics of 2D complex wavelets, constructed from the first, second, and third derivatives of a one-dimensional Gaussian function, are thoroughly examined through theoretical analysis and numerical calculations. These wavelets are then applied to the analysis of low signal-to-noise ratio and low-contrast fringes to reconstruct the 3D surface profile of the object. Using Phase Measuring Profilometry（PMP）results as a reference, the standard deviation（STD）of 3D surface reconstruction errors, based on the three 2D complex Gaussian wavelets developed in this study, remains consistently below 0.07 in planar measurements. For non-uniform reflective surfaces with low signal-to-noise ratio fringes, the 2D WTP demodulation method, employing the proposed wavelets, outperforms both the complex Mexican hat wavelet and the traditional Fan wavelet in terms of reconstruction accuracy. In non-dark-field regions, the reconstruction error STD is maintained below 0.05, effectively enhancing measurement precision. This research not only enriches the wavelet basis function library for 2D WTP but also expands its potential applications in optical measurement and fringe pattern analysis.