There is a building named Souq Al Madina, around 10 to 15 shops are there doing this kind of jobs.

All Car Electrical problems are dealt there. They have second hand parts, Thailand made parts, china made parts.

Based on your budget, you can decide

Exact location of the building can be found in the below link

https://www.google.com/maps/dir/Doha,+Qatar/25.217542,51.4379474/@25.2548295,51.451272,13z/data=!3m1!4b1!4m8!4m7!1m5!1m1!1s0x3e45c534ffdce87f:0x44d9319f78cfd4b1!2m2!1d51.533333!2d25.286667!1m0