We calculate the diffusion barrier of fluorine adatoms on doped graphene in the diluted limit using Density Functional Theory. We found that the barrier Δ strongly depends on the magnitude and character of the graphene's doping (δn): it increases for hole doping (δn < 0) and decreases for electron doping (δn > 0). Near the neutrality point the functional dependence can be approximately by Δ = Δ0- αδn, where α ≃ 6 × 1012meV cm2. This effect leads to significant changes of the diffusion constant with doping even at room temperature and could also affect the low temperature diffusion dynamics due to the presence of substrate induced charge puddles. In addition, this might open up the possibility to engineer the F dynamics on graphene by using local gates.