Time Constraint

I have a date tomorrow at 11AM and she has to see the doctor at 1PM. I am going to her area because she said it was too far to come my area. So I only have a 2 hour window to meet her. Should I try close her within 2 hours or leave it for 2nd date? Or try to meet her again the same day after her doctor's appointment if I am still in the area? Thanks