  We explore a two-qubit system defined on valley isospins of two electrons
confined in a gate-defined double quantum dot created within a MoS$_2$
monolayer flake. We show how to initialize, control, interact and read out such
valley qubits only by electrical means using voltages applied to the local
planar gates, which are layered on the top of the flake. By demonstrating the
two-qubit exchange or readout via the Pauli blockade, we prove that valley
qubits in transition-metal-dichalcogenide semiconductors family fulfill the
universality criteria and represent a scalable quantum computing platform. Our
numerical experiments are based on the tight-binding model for a MoS$_2$
monolayer, which gives single-electron eigenstates that are then used to
construct a basis of Slater-determinants for the two-electron configuration
space. We express screened electron-electron interactions in this basis by
calculating the Coulomb matrix elements using localized Slater-type orbitals.
Then we solve the time-dependent Schr\"odinger equation and obtain an exact
time-evolution of the two-electron system. During the evolution we
simultaneously solve the Poison equation, finding the confinement potential
controlled via voltages applied to the gates.
