Quinlivan has participated in various international exhibitions. In 2016, she exhibited Spatialisation at Pembroke College during the Time and Temporality conference at Cambridge University and toured with Project Field Trip through Singapore, the Philippines, and Indonesia. She performed Immobilised at the Zentrum für Kunst und Urbanistik in Berlin in 2017 and held a solo exhibition, Pellucid , at Colorado State University. In 2018, she presented her solo show Impulses, Restraints, Tones at Jan Kossen Contemporary in New York. In 2019, she was part of MINIARTEXTIL in Como, Italy.
In Australia, Quinlivan has had solo exhibitions at the National Portrait Gallery in Canberra (2020, 2019, and 2016), the Town Hall Gallery in Melbourne (2019), and the Canberra Museum and Art Gallery (2017). She has been featured in group shows like Contour554 in Canberra (2022 and 2020), Drawn to Experience at Queensland College of Art (2015), MOTION at Bega Valley Regional Gallery (2015), and the Australian Print Triennial at Art Vault Mildura (2015).
She has completed public art projects including an artwork for the Frankston Hospital Redevelopment Project 2025, Canberra Hospital Expansion project (2023-2024), the foyer of 80 Anne St, Brisbane (2022), a sandstone engraving and ceramic print on glass at 275 George Street, Sydney (2021), a site-specific installation for Design Canberra, City Walk (2020), and artworks for the Canberra Light Rail Network stations (2018).
Quinlivan was a finalist in the Alice Prize (2018, 2014), the Churchie Art Prize (2017), and the Calleen Art Award (2017). She was an artist in residence at the Art at the Heart Residency, Shire of East Pilbara, and at the Zentrum für Kunst und Urbanistik in 2017, where she was mentored by artist Chiharu Shiota. She received the ANU College of Arts & Social Science Scholarship in 2016, participated in the Jump Mentoring Program through the Australia Council for the Arts in 2014, and received ARTS ACT funding in 2014 to establish a mentoring program for young Canberra arts graduates.
Her work is included in collections such as the National Gallery of Australia, The Australian High Commission in Singapore, ACT Legislative Assembly Art Collection, Arthur & Suzie Roe Collection, Justin Art House Museum, Deakin University Art Collection, The Australian National University, KPMG Art Collection, Shire of East Pilbara, Philip Cox Collection, Ormond College Collection, and various private collections.