Doswellia possesses many highly derived features in its skeleton. The skull is low and elongated with a narrow snout and wide temporal region behind the eye sockets. The temporal region is unusual in that it is euryapsid, which means that the lower of the two temporal holes on either side of the skull has closed. The jugal bone has expanded into the region the lower temporal opening would normally occupy. Paired squamosal bones extend beyond the skull's back margin to form small horn-like projections. The skull of Doswellia lacks several bones found in other archosauriforms, including the postfrontals, tabulars, and postparietals.
The body of Doswellia is also distinctive. The neck is elongated and partially covered by a fused collection of bony scutes called a nuchal plate. The ribs in the front part of the torso project horizontally from the spine and then bend at nearly 90-degree angles to give the body of Doswellia a box-like shape. The blade-like ilium bone of the hip also projects horizontally. The back and underside are covered with ordered rows of bony plates called osteoderms.
The type species, Doswellia kaltenbachi, was described by Weems in 1980. Weems placed Doswellia within Thecodontia, a group of archosaurs that traditionally included many Triassic archosaurs. He placed the genus within its own family, Doswelliidae, and suborder, Dosweliina. Parrish (1993) placed Doswellia among the most primitive of the crurotarsans, a group that includes crocodilians and their extinct relatives. More recently, Dilkes and Sues (2009) proposed a close relationship between Doswellia and the early archosauriform family Proterochampsidae. Desojo et al. (2011) added the Brazilian archosauriforms Tarjadia and Archeopelta to Doswelliidae, and found support for Dilkes and Sues' classification in their own phylogenetic analysis.