Learning Quran is the most easy thing in Qatar Alhamdulillah. You can approch any imam or muazzin at you local masjid and ask them. Either you can opt to go for the Quran classess (tahfiz) which are located in almost every area or ask for their personal time for the same. I personally learnt from the local muazzin in my locality alhamdulillah! You can also approch Fanar for the same.

Its not for Muslims alone, even Non-Muslims are welcome.

Hope it helps.