We present deep H-band surface photometry and analysis of 40 Local Volume galaxies, a sample primarily composed of dwarf irregulars in the Cen A group, obtained using the Infrared Imager and Spectrograph 2 detector at the 3.9-m Anglo-Australian Telescope. We probe to a surface brightness of ~ 25 mag arcsec-2, reaching a 40 times lower stellar density than the Two Micron All Sky Survey (2MASS). Employing extremely careful and rigorous cleaning techniques to remove contaminating sources, we perform surface photometry on 33 detected galaxies deriving the observed total magnitude, effective surface brightness and best-fitting Sérsic parameters. We make image quality and surface photometry comparisons to 2MASS and VISTA Hemisphere Survey demonstrating that deep targeted surveys are still the most reliable means of obtaining accurate surface photometry. We investigate the B - H colours with respect to mass for Local Volume galaxies, finding that the colours of dwarf irregulars are significantly varied, eliminating the possibility of using optical-near-infrared colour transformations to facilitate comparison to the more widely available optical data sets. The structure-luminosity relationships are investigated for our 'clean' sample of dwarf irregulars. We demonstrate that a significant fraction of the Local Volume dwarf irregular population have underlying structural properties similar to both Local Volume and Virgo cluster dwarf ellipticals. Linear regressions to structure-luminosity relationships for the Local Volume galaxies and Virgo cluster dwarf ellipticals show significant differences in both slope and scatter around the established trend lines, suggesting that environment might regulate the structural scaling relationships of dwarf galaxies in comparison to their more isolated counterparts.