We present the high-angular-resolution catalogue for the Australia Telescope 20GHz (AT20G, Cat. J/MNRAS/402/2403) survey, using the high-angular-resolution 6-km antenna data at the baselines of ~4500m of the Australia Telescope Compact Array. We have used the data to produce the visibility catalogue that separates the compact active galactic nuclei (AGNs) from the extended radio sources at the 0.15arcsec angular scale, corresponding to the linear size scale of 1kpc at redshifts higher than 0.7. We find the radio population at 20GHz to be dominated by compact AGNs constituting 77% of the total sources in the AT20G. We introduce the visibility-spectra diagnostic plot, produced using the AT20G cross-matches with lower frequency radio surveys at 1GHz [the NRAO VLA Sky Survey (NVSS, Cat. VIII/65) and the Sydney University Molonglo Sky Survey (SUMSS, Cat. VIII/81)], that separates the 20GHz population into distinct sub-populations of the compact AGNs, the compact steep-spectrum (CSS) sources, the extended AGN-powered sources and extended flat-spectrum sources. The extended flat-spectrum sources include a local thermal emitting population of high-latitude planetary nebulae and also gravitational lens and binary black hole candidates among the AGNs. We find a smooth transition in properties between the CSS sources and the AGN populations. The visibility catalogue, together with the main AT20G survey, provides an estimate of angular size scales for sources in the AT20G and an estimate of the flux arising from central cores of extended radio sources. The identification of the compact AGNs in the AT20G survey provides high-quality calibrators for high-frequency radio telescope arrays and very large baseline interferometry observations.