The time lag between optical and near-infrared continuum emission in active galactic nuclei (AGN) shows a tight correlation with luminosity and has been proposed as a standardisable candle for cosmology. In this paper, we explore the use of these AGN hot-dust time lags for cosmological model fitting under the constraints of the new VISTA Extragalactic Infrared Legacy Survey VEILS. This new survey will target a 9 deg^2 field observed in J- and Ks-band with a 14-day cadence and will run for three years. The same area will be covered simultaneously in the optical griz bands by the Dark Energy Survey, providing complementary time-domain optical data. We perform realistic simulations of the survey setup, showing that we expect to recover dust time lags for about 450 objects out of a total of 1350 optical type 1 AGN, spanning a redshift range of 0.1 < z < 1.2. We use the lags recovered from our simulations to calculate precise distance moduli, establish a Hubble diagram, and fit cosmological models. Assuming realistic scatter in the distribution of the dust around the AGN as well as in the normalisation of the lag-luminosity relation, we are able to constrain {Omega}_{Lambda} in {Lambda}CDM with similar accuracy as current supernova samples. We discuss the benefits of combining AGN and supernovae for cosmology and connect the present work to future attempts to reach out to redshifts of z > 4.
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