Can you and your spouse stay at their own parents place right after nikah?

Assalamualaikum I want to know is it possible that I can stay at my place and she can stay at her place right after the actual nikah (After signing the marriage contract) until the time comes? Cause I don't want to have a Haram relationship with her. And I am in love with her. So I want to have a halal relationship. But we are still really young and still am a student (I am still just 18) so I was wondering if it was possible that I can make the relationship halal but stay at my place and she can stay at her place and when the time is right we can arrange a traditional marriage ceremony or feast few years after the actual nikah. Is that possible?