All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is confirmed in the authentic Sunnah of the Prophet that it is desirable to pray two Rak'ahs in the mosque when returning from a journey.
Ka'b Ibn Maalik narrated in the story of the battle of Tabook saying: "Whenever the Prophet returned from a journey, he used to stop at the mosque and perform two Rak'ahs." [Al-Bukhari and Muslim]
Imaam An-Nawawi said: "This prayer is intended for coming back from travel and one should intend with it the prayer of returning from travel."
As regards praying two Rak'ahs before setting out for a journey, then we do not know any authentic evidence about it, as there are some Ahadeeth about it which are classified as weak.
However, some scholars are of the view that it is desirable to pray two Rak'ahs before setting out on a journey.
With regard to the Centres of memorization of the Quran (in Qatar), you may contact the Ad-Da'wah Department in the Ministry of Endowment and Islaamic Affairs for details.
Allaah Knows best.