Circumnuclear star formation and AGN feedback is believed to play a critical role in the context of galaxy evolution. The low-luminosity QSO (LLQSO) sample that contains 99 of the closest AGN with redshift z<=0.06 fills the gap between the local AGN population and high-redshift QSOs that is essential to understand the AGN evolution with redshift. In this paper, we present the results of near-infrared H+K-integral field spectroscopy of the inner kiloparsecs of the LLQSO HE 1029-1831 with SINFONI. Line maps show that ionized hydrogen gas is located in spiral arms within the stellar bar and in a circumnuclear ring. Line fluxes and diagnostic line ratios indicate recent or ongoing star formation in the circumnuclear region and the presence of young and intermediate-age stellar populations in the bulge. In particular, we find traces of an intense starburst in the circumnuclear region that has begun around 100 Myr ago but has declined to a fraction of the maximum intensity now. We estimate the dynamical bulge mass and find that the galaxy follows published M_BH-M_bulge relations. However, bulge-disk decomposition of the K-band image with BUDDA reveals that HE 1029-1831 does not follow the M_BH-L_bulge relations of inactive galaxies. We conclude that the deviation from M_BH-L_bulge relations of inactive galaxies in this source is rather caused by young stellar populations and not by an undermassive black hole.