If the time remaining for the Prayer is very short that if you don't hurry up, you will or might miss performing the Prayer within its time, then you must hurry up to perform the Prayer within its time. If the sunrise is very near and you need to perform your Morning Prayer, you must do everything possible to perform it before sunrise. No doubt, you must perform all the obligatory acts and recitations of Salat, but don't spend time in recommended acts or recommended recitations which might make you miss performing the Prayer before sunrise.
Even reciting a Sura after Sura Al Hamd cab be dropped if there is no time for it before sunrise.
If there is an emergency like saving life or urgent help required, you can also hurry up. In fact we are allowed to terminate Salat to save life.
We should not hurry up in our Salat for any worldly matter. The Hadeeth says: No work can succeed before performing the obligatory Salat.
Speedy Salat for worldly reason is very bad and it is from the acts of hypocrites and sinners. The Prophet (SAWA) said when he saw a person who was praying speedy Salat: If this person dies with such Salat, will not die in my religion.