well please at least fuse it under the hood, that way when the coating on the wire starts wearing through and it touches a ground source (somewhere where your door or hood touches it) it will pop the fuse, and not start your car on fire, or make the battery explode.
I am not saying "don't do this yourself" but if you are questioning if something is right or not, maybe you should have someone help you in person that knows what they are doing.
although it may seem that stereo stuff is easy to do, there is still the potential to ruin your stereo by hooking a power wire to a speaker wire by accident.
a good example of this is when my friend had another buddy who claimed he could install the stereo in a 1991 olds toronado. Well he got it hooked up and as soon as they turned on the key, the instrument cluster quit working. $400 later, when a new cluster was put in he opted not to let the other guy install it.
I am not trying to discourage you, but you really need to look at what you are doing. taking shortcuts (like the amp wire through the door) may save some time getting it hooked up, but might cause other problems later on.
just my opinion of course