The study of dust above the lunar surface is important for both science and technology. Dust particles are electrically charged due to impact of the solar radiation and the solar wind plasma and, therefore, they affect the plasma above the lunar surface. Dust is also a health hazard for crewed missions because micron and sub-micron sized dust particles can be toxic and harmful to the human body. Dust also causes malfunctions in mechanical devices and is therefore a risk for spacecraft and instruments on the lunar surface. Properties of dust particles above the lunar surface are not fully known. However, it can be stated that their large surface area to volume ratio due to their irregular shape, broken chemical bonds on the surface of each dust particle, together with the reduced lunar environment cause the dust particles to be chemically very reactive. One critical unknown factor is the electric field and the electric potential near the lunar surface. We have developed a modelling suite, Dusty Plasma Environments: near-surface characterisation and Modelling (DPEM), to study globally and locally dust environments of the Moon and other airless bodies. The DPEM model combines three independent kinetic models: (1) a 3D hybrid model, where ions are modelled as particles and electrons are modelled as a charged neutralising fluid, (2) a 2D electrostatic Particle-in-Cell (PIC) model where both ions and electrons are treated as particles, and (3) a 3D Monte Carlo (MC) model where dust particles are modelled as test particles. The three models are linked to each other unidirectionally; the hybrid model provides upstream plasma parameters to be used as boundary conditions for the PIC model which generates the surface potential for the MC model. We have used the DPEM model to study properties of dust particles injected from the surface of airless objects such as the Moon, the Martian moon Phobos and the asteroid RQ36. We have performed a (v0, m/q)-phase space study where the property of dust particles at different initial velocity (v0) and initial mass per charge (m/q) ratio were analysed. The study especially identifies regions in the phase space where the electric field within a non-quasineutral plasma region above the surface of the object, the Debye layer, becomes important compared with the gravitational force. Properties of the dust particles in the phase space region where the electric field plays an important role are studied by a 3D Monte Carlo model. The current DPEM modelling suite does not include models of how dust particles are initially injected from the surface. Therefore, the presented phase space study cannot give absolute 3D dust density distributions around the analysed airless objects. For that, an additional emission model is necessary, which determines how many dust particles are emitted at various places on the analysed (v0, m/q)-phase space. However, this study identifies phase space regions where the electric field within the Debye layer plays an important role for dust particles. Overall, the initial results indicate that when a realistic dust emission model is available, the unified lunar based DPEM modelling suite is a powerful tool to study globally and locally the dust environments of airless bodies such as planetary moons, Mercury, asteroids and non-active comets far from the Sun.