We report on the first femtosecond vertical external cavity surface emitting laser (VECSEL) exceeding 1 W of average output power. The VECSEL is optically pumped, based on self-assembled InAs quantum dot (QD) gain layers, cooled efficiently using a thin disk geometry and passively modelocked with a fast quantum dot semiconductor saturable absorber mirror (SESAM). We developed a novel gain structure with a flat group delay dispersion (GDD) of ± 10 fs2 over a range of 30 nm around the designed operation wavelength of 960 nm. This amount of GDD is several orders of magnitude lower compared to standard designs. Furthermore, we used an optimized positioning scheme of 63 QD gain layers to broaden and flatten the spectral gain. For stable and self-starting pulse formation, we have employed a QD-SESAM with a fast absorption recovery time of around 500 fs. We have achieved 1 W of average output power with 784-fs pulse duration at a repetition rate of 5.4 GHz. The QD-SESAM and the QD-VECSEL are operated with similar cavity mode areas, which is beneficial for higher repetition rates and the integration of both elements into a modelocked integrated external-cavity surface emitting laser (MIXSEL).