My answer on Can we recite two or more surahs in one rakat when praying? is more general but you can recite what you want. You even can repeat in each rak'a the same verse or surah, it is up to you and what is easier for you. Of course there are some limitation for example in the fatwa I linked as a reference at the bottom of this answer somebody asked whether praying with surat al-fatiha and surat al-ikhlass (112) in each rak'a with a augmenting amount of re-reciting al-Ikhlass each time: For example reciting surat al-Ikhlass in a rak'a re-reciting it or reciting it three times in an other rak'a etc. This was considered as a bid'ah (consult the fatwa for a detailed explanation).
The most important in any prayer is that you are asked to
...recite of what you know of the Qur'an,... (See for example sahih al-Bukhari)
Of course you can also take a moshaf (hard copy of the qur'an) at hand and read from it (See Can we read straight from the Quran when we stand up for salat?), but it's the best to do what ever comforts you!
The point is if you pray at night you should do your best and doing it right and without haste (feel at ease or rest while prostrating, bowing sitting and standing) as you might be alone and it's a good time to do conversation with your Creator and Lord in a kind "of intimate atmosphere"!
This fatwa is covering your issue more or less explicitly.
And Allah knows best!
