Plasmon-polaritons are among the most promising candidates for next generation optical sensors due to their ability to support extremely confined electromagnetic fields and empower strong coupling of light and matter. Here we propose quantum plasmonic immunoassay sensing as an innovative scheme, which embeds immunoassay sensing with recently demonstrated room temperature strong coupling in nanoplasmonic cavities. In our protocol, the antibody-antigen-antibody complex is chemically linked with a quantum emitter label. Placing the quantum-emitter enhanced antibody-antigen-antibody complexes inside or close to a nanoplasmonic (hemisphere dimer) cavity facilitates strong coupling between the plasmon-polaritons and the emitter label resulting in signature Rabi splitting. Through rigorous statistical analysis of multiple analytes randomly distributed on the substrate in extensive realistic computational experiments, we demonstrate a drastic enhancement of the sensitivity up to nearly 1500% compared to conventional shifting-type plasmonic sensors. Most importantly and in stark contrast to classical sensing, we achieve in the strong-coupling (quantum) sensing regime an enhanced sensitivity that is no longer dependent on the concentration of antibody-antigen-antibody complexes -- down to the single-analyte limit. The quantum plasmonic immunoassay scheme thus not only leads to the development of plasmonic bio-sensing for single molecules but also opens up new pathways towards room-temperature quantum sensing enabled by biomolecular inspired protocols linked with quantum nanoplasmonics.