This paper investigates distributed Dominating Set (DS) and Connected Dominating Set (CDS) construction in dynamic wireless networks under the SINR interference model. Specifically, we present a new model for dynamic networks that admits both churns (due to node arrivals/departures) and node mobility. Under this dynamic model, we propose efficient algorithms to construct a DS and a CDS with constant approximation ratios w.r.t. the corresponding minimum ones in O(log n) time with a high probability guarantee. To the best of our knowledge, these algorithms are the first known ones for DS and CDS construction in dynamic networks assuming the SINR interference model. We believe our dynamic network model can greatly facilitate distributed algorithm studies in mobile and dynamic wireless networks.