I like to pray the prayers of night. So I wake up half an hour before the Fajr prayer and I pray, then I finish it by Witr. Then I read Qur'an for 10 minutes before the morning prayers. Is this correct?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

May Allah bless you and help you to keep on doing more good deeds. Know that the prayers at night and reciting the Qur'an are among the best actions that bring one nearer to Allah, due to their great reward and other virtues.
We do ask Allah, The Great and Almighty, to help all of us to keep on doing more Zikr Praise Him and as worship Him well.
If you can wake up at the sixth part of night to increase your worship that will be better and more beneficial.
Allah knows best.