The original box on the side says, "EACH AMIGA 1000 PERSONAL COMPUTER COMES COMPLETE WITH:" (and the box says "Copyright (c) 1985" and "Printed in Japan"). The bottom of the keyboard says, "KEYBOARD FOR MODEL 1000" (red A keys). The power supply says 1985, but I think this Amiga was made in very early 1986.
Nowhere does it say "A1000", just "1000".