The Galactic Centre (GC) region is a highly interesting region for very high energy gamma-ray studies due to its proximity and diverse sources. It is also a unique place for Dark Matter (DM) searches, since we expect a large amount of DM in this region and it is nearby. Currently a new detector is under development to observe the GC region, called the Southern Wide field-of-view Gamma-ray Observatory (SWGO). This instrument will be the first water Cherenkov detector located in the Southern Hemisphere sensitive to >100 GeV gamma rays. In our work, we are going to present a simulation of the GC gamma-ray mission as seen by a SWGO-like observatory. To do so we are using the models published by the Cherenkov Telescope Array (CTA) Collaboration together with simulated Instrument Response Functions (IRFs) for testing purposes. This also allows us to predict the expected sensitivity of SWGO to WIMP DM annihilations using a template based method. A sensitivity study during the design phase of the observatory is important in order to choose the best detector design to get outstanding physics results.