High harmonic generation (HHG) in graphene quantum dots of armchair edge by strong coherent electromagnetic radiation taking into account collective electron-electron scattering as well in such nanosystems is considered. The microscopic quantum theory describing the plane quantum dot-laser field nonlinear interaction within the dynamic Hartree–Fock approximation is developed. The many-body Coulomb interaction is considered in the extended Hubbard approximation. The obtained results indicate the significance of the nanostructure lateral size, shape, and bandgap width in HHG process that allows to increase in the quantum yield of high-order harmonics and the cutoff photon energy.