The only word that comes to my mind is tiptoe. However, this word implies that you are walking stealthily or cautiously.
Is there a word that just means to walk slowly?
Without knowing what I was doing, I _ toward her.
I would suggest amble:
- to go at a slow, easy pace; stroll; saunter:
- a slow, easy walk or gentle pace.
Your sentence would then be:
Without knowing what I was doing, I ambled toward her.
As that definition suggests, strolled or sauntered may also work for you.