2D DWT computation order
For each single level of a isotropic or square DWT, the row/column order is not important.  Note however that there exists an alternative decomposition, termed anisotropic, rectangular, that does all rows first, then all columns (or the converse) which results in a different subband organization. This is described in the overview of 2D wavelets: A panorama on Multiscale Geometric Representations (arxiv) in Section 3: 2.3.2. Separable orthogonal wavelets.

[EDIT: Added references to related questions]


2D DWT Image Issue
What is the correct order of operations for a 2D Haar wavelet decomposition?
2D DWT computation order