I can only speak from experience and give my own opinion, which is, feel free to read ahead but be careful about delving too deeply into memorizing the material. A & P is a very complex topic with tons of material, and your professor will probably narrow down the details that you need to know. Reading ahead to get a general feel for the basic concepts and the textbook's style is never a bad idea, but I wouldn't go too overboard trying to memorize details yet. Wait to see what the prof considers important and wants you to know.
Now that I think about it, there is one thing that you will need to know and could get a start on now: understanding the anatomical position and some of the directional terms related to it (proximal/distal, anterior/posterior, etc.) These should all be outlined in your book, and you will definitely use them. Below is a page that outlines some of the concepts for you:
I really enjoyed A & P--lots to learn, but it's very interesting...and you can use your own body for an exam cheat sheet! The proctors in my school's testing center love it when A & P students come to take exams--they're always feeling their heads, staring at their hands, flexing their joints, you name it*
*edited to add: not doing this stuff to the proctors, obviously, but the students doing it to themselves