One of the key challenges to move single-photon sources into practical applications is the ability to efficiently extract light from a single quantum emitter while maintaining efficient photon emission. Here, we propose to harness the optical topological transitions of graphene-hBN hyperstructure to engineer the emission from quantum emitters and achieve preferential power extraction. We have designed a hyperstructure, which possesses tunability of spontaneous emission and enhancement of extraction during optical topological transitions from the closed (ellipsoid) isofrequency surface to an open (hyperboloid) isofrequency surface by tuning the chemical potential of graphene. Such an interesting feature relies exclusively on the hyperbolic properties of hBN and tunable behavior of graphene, which is confirmed by detailed calculations and simulations. Remarkably, single-photon sources based on the hyperstructure do not require overmuch microfabrication and they are capable of working at tunable frequency.