This paper evaluates the impact of fiducial cosmology on the Baryon Acoustic Oscillations (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) survey Data Release 1 (DR1). The study uses a suite of mock galaxy catalogues with realistic survey properties, including bright galaxies, luminous red galaxies, emission line galaxies, and quasars, spanning a redshift range from 0.1 to 2.1. Four secondary cosmologies from the ABACUSSUMMIT set are compared against DESI's fiducial cosmology (Planck 2018). The secondary cosmologies include lower cold dark matter density, a thawing dark energy universe, a higher number of effective species, and a lower amplitude of matter clustering. The mocks are processed through the BAO pipeline, and the systematic contribution to the error in the dilation parameters $\alpha_{\text{iso}}$ and $\alpha_{\text{AP}}$ is determined to be conservative at 0.1%. The impact of the fiducial cosmology on DESI DR1 data is then directly tested. The results show that the best-fit BAO scales are highly correlated between Fourier and configuration space, and the residual differences are uncorrelated, indicating no systematic bias. The systematic error budget due to the fiducial cosmology is estimated to be 0.1%. The study also investigates the separate contributions of grid and template cosmologies, finding that the thawing dark energy cosmology introduces the largest dispersion in the differences.This paper evaluates the impact of fiducial cosmology on the Baryon Acoustic Oscillations (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) survey Data Release 1 (DR1). The study uses a suite of mock galaxy catalogues with realistic survey properties, including bright galaxies, luminous red galaxies, emission line galaxies, and quasars, spanning a redshift range from 0.1 to 2.1. Four secondary cosmologies from the ABACUSSUMMIT set are compared against DESI's fiducial cosmology (Planck 2018). The secondary cosmologies include lower cold dark matter density, a thawing dark energy universe, a higher number of effective species, and a lower amplitude of matter clustering. The mocks are processed through the BAO pipeline, and the systematic contribution to the error in the dilation parameters $\alpha_{\text{iso}}$ and $\alpha_{\text{AP}}$ is determined to be conservative at 0.1%. The impact of the fiducial cosmology on DESI DR1 data is then directly tested. The results show that the best-fit BAO scales are highly correlated between Fourier and configuration space, and the residual differences are uncorrelated, indicating no systematic bias. The systematic error budget due to the fiducial cosmology is estimated to be 0.1%. The study also investigates the separate contributions of grid and template cosmologies, finding that the thawing dark energy cosmology introduces the largest dispersion in the differences.