I was wondering if I could have my Destiny character on two of the same system because I started playing on my brothers ps4 because I was getting my own next month. when I get my own ps4 can I port my destiny character on my brothers ps4 to my own ps4?
Yes, provided you log in with the same PSN account.
If you have been using your brothers PSN account on his PS4, then you will need to log in with his PSN account in order to continue using your character - I'm unsure of the effects of that (whether he will be able to continue playing or not). If you have been using your own PSN account on his PS4, then you'll just use that.