Qarshe was born in 1924 in the Somali expatriate community in Moshi, Tanzania. He belonged to the Muuse Carre sub clan of Habar Yoonis (Isaaq) that mainly inhabits Sanaag region of Somaliland. In 1931, at the behest of his family, he left Tanzania and settled in Aden, Yemen for his education. It is in Aden where Abdullahi had his first encounter with cinema and radio playing western films and Indian and Arabic music, which inspired him to buy a lute to accomplish his new goal of creating music in the Somali language. He was married to Adaiya Qarshe whom he had four children with, Rukiyo Qarshe, Safiyo Qarshe, Anab Qarshe and Mahad Qarshe.
Qarshe, along with other first generation artists such as Ali Feiruz and Mohamed Nahari, was among the pioneers of modern Somali music.
An innovative musician, Qarshe often employed a wide variety of instruments in his art, such as the guitar, piano and oud. He was also known for his poems and his theatrical work at Mogadishu and Hargeisa venues.
In addition, Qarshe was a member of the pioneering Somali musical ensemble Waaberi.