Is it possible to cast Plane Shift on a dead body?
There is no official ruling for that
And be glad about it. Let me explain.
The developers of Pathfinder simply cannot answer that question without breaking the entire game. Since Pathfinder was built on 3.5's OGL, it inherited many problems with it, one of those problems is the proper definition of a corpse.
While there are many spells that target directly a corpse (Gentle Repose) and is crystal clear on what it should do with the targeted corpse, we also have spells that target only creatures (Reduce Person), or spells that target only objects (Shrink Item), or spell that targets both (Fireball). And sometimes we don't know how those effects should affect a corpse, sometimes it makes (logical) sense, but sometimes it doesn't.
Defining corpses to be objects would break half of those spells. Defining corpses to be creatures would break another half. And defining them to be neither would break half of both halves. For example, if you say that they are neither objects nor creatures, a fireball simply cannot damage a corpse.
What happens to a wizard when he is killed under the effects of the Fly spell? The spell only target's creatures, if he is no longer a creature he shouldn't be a valid target for the spell and his corpse should splatter against the ground? I know one instance where I simply let the corpse fall down slowly as if the duration had expired, so the party could recover the body.
And that's only about spells, we also have magic items, feats and special abilities that refer to creatures or objects, and without a proper definition, the rules can lead to weird situations, like a t-rex swallowing an adventurer and have a terrible indigestion because the adventurer's corpse cannot take further damage inside their belly.
You can't move through a square occupied by an opponent unless the opponent is helpless. You can move through a square occupied by a helpless opponent without penalty. Some creatures, particularly very large ones, may present an obstacle even when helpless. In such cases, each square you move through counts as 2 squares.
Essentially, you cannot make an official ruling on what to consider a corpse to be, so that is left entirely at GM fiat. Make a ruling on a case by case basis, check the situation, consider what you think would work best for the game and stick with that.
Personally, I would rule that you can transport corpses using Plane Shift, as the intent of the spell isn't to harm or buff those creatures, but to allow interplanar travel, and even if it doesn't make sense from what is written on the spell, you are causing extra (and probably unnecessary) complications by not allowing the caster to transport his dead friends elsewhere. They would have to find a portable hole, or a bag of holding (which they probably already have), or even remove some carried weight and treat the corpse as gear so they are transported with her. And that probably isn't fun nor moves the story forward.
The target of the spell Plane Shift is defined as a "creature" (rather than an object.)
As the guide "Hey Can I Chan" linked said, whether a dead body is defined as a creature or an object is not explicitly stated by the rules of Pathfinder and therefore might be left to DM Fiat.
However, there was a ruling in D&D 3.5 FAQ (p.6) that says the answer is no. Seeing as Pathfinder was designed to be backwards compatible with D&D 3.5e (on which it was based, under the OGL) it seems logical to assume the answer would be no, unless the DM wants it otherwise.
However, a corpse could be carried by someone you Plane Shift if it is light enough.