Quantum dots are widely recognized for their advantageous light-emitting properties. Their excitonic fine structure along with the high quantum yields offers a wide range of possibilities for technological applications. However, especially for the case of colloidal QDs, there are still characteristics and properties which are not adequately controlled and downgrade their performance for applications which go far beyond the simple light emission. Such a challenging task is the ability to manipulate the energetic ordering of exciton and biexciton emission and subsequently control phenomena such as Auger recombination, optical gain and photon entanglement. In the present work we attempt to engineer this ordering for the case of InP QDs embedded in polymer matrix, by means of their size, the dielectric confinement and external electric fields. We employ well tested, state of the art theoretical methods, in order to explore the conditions under which the exciton-biexciton configuration creates the desired conditions either for optical gain or photon entanglement. Indeed, this appears to be feasible for QDs with small diameters (1 nm, 1.5 nm) embedded in a host material with high dielectric constant and additional external electric fields. These findings offer a new design principle which might be complementary to the well-established type II core-shell QDs approach for achieving electron-hole separation.