Considering the meaning of destiny, we can change our destiny with Du'a. What if I want something so much but I don't know if it's good for me or not? And Allah knows the best, so what he has pre-scheduled for me is the best. So I should stop making Du'a for what I want to get what Allah wants for me? Because if I insist on it Allah changes my destiny and and the new destiny may ruin my life!?
First of all, in case if you are not sure that certain thing is good for you or not, then islam gives you a solution as Istakhara. Perform the istahkara (pray 2 rakah salah, and recite the dua of istakhara and repeat it for 3 or 7 times), then after that, take the decision you want to make that you should go for doing Dua for it or not.
Istakhara is to ask guidance from Allah, and as only Allah knows what is best for us, we can call Him directly (through istakhara) and ask him to tell us what is best for us.
Here is details about how to perform istakhara, and what it is:
And Allah knows the best
First thing you should know and understand is this...
Whosoever desires (with his deeds) the reward of the Hereafter, We give him increase in his reward, and whosoever desires the reward of this world (with his deeds), We give him thereof (what is written for him), and he has no portion in the Hereafter. (Qur'an 43:20).
Even though it is very compelling to make Du'a for the sake of this present life, we must try to avoid it.
...But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah Knows, while you know not. (Qur'an 2:216)
So, it is better to leave for God to decide the fate of this world, and try to make Du'a asking forgiveness and try to make this Du'a instead...
Our Lord! Give us good in this world and good in the Hereafter, and defend us from the torment of the Fire!"
May the creator guide us all.