JM is correct.
A word of further explanation. People get confused about the DH because they think of him as a kind of offensive substitute. That's not right: the DH and the defensive player for whom he bats are both locked into a spot in the lineup, and
neither is an eligible substitute.
"A substitute is a player who is eligible to replace another player
already in the lineup." (2-36) This definition implies that anyone listed in the lineup is NOT an eligible substitute, and thus may NOT bat in another spot in the order.
FED permits a team to continue with 8 in the lineup when an eligible substitute is not available, as JM points out. That said, I'm fairly confident that
around here everyone would expect the umpires to bend the rules a little and allow the DH to bat in the spot vacated by the injured player. You know, "it's for the kids, blue," "aw, let 'em play, blue..." etc. etc.
