"I am walking to the door."
Translation:Je marche vers la porte.
"vers" means "toward" (in the direction of).
"à la porte" does not work with verb marcher but you can say : "je frappe à la porte" (I knock on the door).
I did some restricted searches on google (with double quotes). "Je march à la porte" got 6000+ hits, whereas "je march ver la porte got 1000+ hits. That suggests that the former is correct.
With the right spelling, indeed "je marche vers la porte" is correct.
Thanks, I wander if it is possible to figure out which verb goes with what in French! Rather peculiar logic, if there is one at all, it seems!