According to literature uterus does express AQP1. According to Uniprot.org, AQP1 is expressed in right lung, retinal pigment epithelium, uterus, mesangial cell, brain, articular cartilage, among other tissues. Regarding which tissues have AQP1 expression, here are a few articles citing expression in various tissues:
Articular cartilage, Pubmed ID: 2007592, 1373524
Brain, Pubmed ID: 15489334
Mesangial cell, Pubmed ID: 14702039
Retinal pigment epithelium, Pubmed ID: 8703970
Uterus, Pubmed ID: 7517253