>but she's very introverted, she needs her own space a lot and she also feels the need to follow plans and routines in a way that's very at odds with how I am.

Honestly, she might just prefer staying at her own home. I am incredibly introverted and even when I was dating someone I loved, I still wanted to sleep in my own bed most nights. I can't get a restful sleep sharing a bed with someone else. Offering her the drawer is very sweet and I think ensuring she has the things she needs to be comfortable at your place is a great idea, but she still may need her alone time in her own space.