The complex dynamics of asymptotic giant branch (AGB) stars and the resulting stellar winds have a significant impact on the measurements of stellar parameters and amplify their uncertainties. Three-dimensional (3D) radiative hydrodynamic (RHD) simulations of convection suggest that convection-related structures at the surface of AGB star affect the photocentre displacement and the parallax uncertainty measured by Gaia. We explore the impact of the convection on the photocentre variability and aim to establish analytical laws between photocentre displacement and stellar parameters to retrieve such parameters from the parallax uncertainty. We used a selection of 31 RHD simulations with CO5BOLD and the post-processing radiative transfer code Optim3D to compute intensity maps in the Gaia G band [320-1050nm]. From these maps, we calculated the photocentre position and temporal fluctuations. We then compared the synthetic standard deviation to the parallax uncertainty of a sample of 53 Mira stars observed with Gaia. The simulations show a displacement of the photocentre across the surface ranging from 4 to 13% of the corresponding stellar radius, in agreement with previous studies. We provide an analytical law relating the pulsation period of the simulations and the photocentre displacement as well as the pulsation period and stellar parameters. By combining these laws, we retrieve the surface gravity, the effective temperature, and the radius for the stars in our sample. Our analysis highlights an original procedure to retrieve stellar parameters by using both state-of-the-art 3D numerical simulations of AGB stellar convection and parallax observations of AGB stars. This will help us refine our understanding of these giants.