Well in chapter nine Doctor Manhattan gains a newfound respect for human life. Therefore, at the end he doesn't want Rorschach to go and make everyone's death useless by telling everyone about Veidt's plan and starting the cold war again.
See, this part still bugs me, too. The Doc respects human life again -- so he goes and kills
1. What little credibility Rorschach ever had with anyone probably went out the window with the arrest/imprisonment, the public release of his true identity, and his landlady's accusations. People thought he was crazy before; who would listen to him now? Especially if it's his word against Golden Boy Adrian Veidt. Really, would it be any kind of question at all?
2. Once again, the sticky wicket: how did anyone expect Rorschach to get back? Walking? Or was the Doc pre-emptively getting rid of Rorschach so he wouldn't have to also get rid of Dan and maybe Laurie later?
3. The Doc told Veidt he neither condemned nor condoned his actions. If that were really true -- especially considering what he tells him later -- he would just walk away without doing anything at all. Nothing to stop the plan; nothing to protect the plan.
4. Manhattan tells Veidt, "Nothing ever ends." He knew the peace wouldn't last. What Veidt's "achieved" is just as impermanent as that of his namesake, Ozymandias. (And while Moore uses lines from the Shelley sonnet in the GN, Horace Smith's sonnet is also telling. http://en.wikipedia.org/wiki/Ozymandias
) So, from a cosmic point of view, what's the point of killing Rorschach?
5. I can't argue with the thought that Manhattan was basically putting Rorschach out of his misery. Think of it: he's spent his life punishing the wicked on behalf of the innocent. Veidt comes along and just kills thousands, regardless of what they've done. And that's just the tip of the iceberg as far as Rorschach's issues go. The hell of it is, just like the citizens who'd gathered to stop the fight just before the squid went splat, Rorschach had been on the path to finding his humanity again.
Er, I had more, but the reply feature's gone wonky on me, so y'all have lucked out.