Dynamic SLAM methods jointly estimate for the static and dynamic scene components, however existing approaches, while accurate, are computationally expensive and unsuitable for online applications. In this work, we present the first application of incremental optimisation techniques to Dynamic SLAM. We introduce a novel factor-graph formulation and system architecture designed to take advantage of existing incremental optimisation methods and support online estimation. On multiple datasets, we demonstrate that our method achieves equal to or better than state-of-the-art in camera pose and object motion accuracy. We further analyse the structural properties of our approach to demonstrate its scalability and provide insight regarding the challenges of solving Dynamic SLAM incrementally. Finally, we show that our formulation results in problem structure well-suited to incremental solvers, while our system architecture further enhances performance, achieving a 5x speed-up over existing methods.