Until 1966, Qatar used the Indian rupee as its currency, in the form of Gulf rupees. When India devalued the rupee in 1966, Qatar, along with the other states using the Gulf rupee, chose to introduce its own currency.
Before doing so, Qatar briefly adopted the Saudi riyal, then introduced the Qatar and Dubai riyal following the signing of the Qatar-Dubai Currency Agreement on 21 March 1966. The Saudi riyal was worth 1.065 Gulf rupees, whilst the Qatar and Dubai riyal was equal to the Gulf rupee prior to its devaluation.
Following Dubai’s entry into the United Arab Emirates, Qatar began issuing the Qatari riyal separate from Dubai on 19 May 1973. The old notes continued to circulate in parallel for 90 days, at which time they were withdrawn.
For a wider history surrounding currency in the region, see the history of British currency in the Middle East.