In this study, we proposed a novel method for extracting the instantaneous respiratory rate (IRR) from the pulse oximeter photoplethysmogram (PPG). The method was performed in three main steps: (1) a time-frequency transform called synchrosqueezing transform (SST) was used to extract the respiratory-induced intensity, amplitude and frequency variation signals from PPG, (2) the second SST was applied to each extracted respiratory-induced variation signal to estimate the corresponding IRR, and (3) the proposed peak-conditioned fusion method then combined the IRR estimates to calculate the final IRR. We validated the implemented method with capnography and nasal/oral airflow as the reference RR using the limits of agreement (LOA) approach. Compared to simple fusion and single respiratory-induced variation estimations, peak-conditioned fusion shows better performance. It provided a bias of 0.28 bpm with the 95% LOAs ranging from -3.62 to 4.17, validated against capnography and a bias of 0.04 bpm with the 95% LOAs ranging from -5.74 to 5.82, validated against nasal/oral airflow. This algorithm would expand the functionality of a conventional pulse oximetry beyond the measurement of heart rate and oxygen saturation to measure the respiratory rate continuously and instantly.