I can start with a quick answer and perhaps others follow up. In short there is not much similarity. A quantum dot is a zero dimensional object realized in semiconductor heterostructures where the electrons are confined in all three dimensions such that the form standing waves similar to the situation in atoms. You can look at a quantum dot as an artificial atom. A qubit is an object from quantum information theory. It says nothing about how you realize it. The hallmark of a qubit are coherent super position states, e.g., of spin down and spin up. Quantum dots are sometimes discussed as possible solid state realizations of qubits. 

Thank you Christian Binek.

If the degree of freedom for an electron is restricted by all 3D cordinates in your nano materiel then it is known as zero dimensional quantum dot... If your size of the nano particle is comparable with the Bohr exciton radius ....then that nano particle shows quantum confinement also....! 

The qubit is completely related to Quantum mechanical entity it doesn't have any relation with Quatum dots....!