brother i see no reason why not, it is fard to perform the prayer therefore you MUST get up for it but if you do not want to pray more after its up2u. However i find it best to wake up an hour before fajr to pray tahajjud for when you pray tahajjud Allah descends into the lowest heaven to hear who is repenting or asking nething of him so that he may concede to there request! (sahih bukhari), so inshaAllah if u wish to do extra do that