How can I do quantum chemistry with QED?

From a theoretical chemists point of view, the inclusion of Quantum Electrodynamics (QED) can be very interesting if you are interested in radiaton-matter interactions, where the radiation field is quantized (commonly in the Coulomb gauge leading to a non-covariant quantization). This would include all types of absorption and emission processes but additionally also intermolecular dipole-dipole coupling, for example. If you are interested in this topic, I can highly recommend the textbook on Molecular Quantum Electrodynamics by Craig and Thirunamachandran.

Additionally, there is a very fascinating field studying atoms and molecules in cavities, i.e. in the framework of cavity-QED. In this context, a whole bunch of interesting new phenomena emerge, e.g. the Born-Oppenheimer-approximation needs to be reformulated, due to the full quantum description of the radiation field and the molecular degrees of freedom. You can consider, if you are interested in getting an idea of this subject.