The ALPACA experiment is a new air shower experiment mainly aiming to explore the southern sky in the VHE gamma-ray regime beyond 100 TeV. As the prototype experiment, ALPAQUITA will start in late 2021. It consists of a surface air shower array (18,450 ${\rm m}^2$) and an underground muon detector array (900 ${\rm m}^2$). In this study, the performance of ALPAQUITA including the sensitivity to gamma-ray point sources is investigated using a Monte Carlo simulation to quantitatively evaluate the possibility of detection of gamma-ray sources in the prototype phase. Corsika 7.6400 and Geant4 v10.04.p02 are used to simulate air shower development in the atmosphere and detector response, respectively. The output data are then processed and analyzed in the same way as the experiment. As a result, the study finds that the air shower array has an energy resolution of $\pm21\%$ and the angular resolution of $\simeq 0.2^{\circ}$ for gamma rays with an energy of 100 TeV. The detection area of the air shower array for gamma rays reaches $\simeq 12, 600 \, {\rm m}^2$ above $\simeq 10\, {\rm TeV}$. The muon detector rejects $\simeq 99.9\%$ of background cosmic rays and maintains $\simeq 80\%$ of signal gamma rays. This high discrimination power will enable the detection of five southern known gamma-ray sources beyond 30 TeV and the extension of the energy spectrum of one out of the five, HESS J1702-420A, up to $\simeq 300\, {\rm TeV}$ during one calendar year observation. This study concludes that ALPAQUITA will provide data enough to discuss a hot topic of VHE gamma-ray astronomy before passing the baton to ALPACA.