I'm no expert, and I haven't read Watchmen in a while, but yeah I think Dr. Manhattan can sense past, present, and future at the same time but he can't change it.

But it's not just him. His wife tried to change events too. Shouldn't that have an effect on the timeline?

I am actually Reading Watchmen right now and I read Doomsday Clock so I know a little bit. I preceded it Like this:

Dr. Manhattan could Change the Timeline (Like in doomsday Clock explained) but he simply doesn't want to, because he doesn't care. He is no normal human for example (Doomsday Clock "Spoiler") in Doomsday Clock he killed people Just to See how the World will Change. He played with lives, but for him it was only a "experiment" (Spoiler End). In the Watchmen Comic He knew that JFK will get murdered but simply didnt Change it or he could prevent the Comedian From killing an innocent Woman but didnt do it. The Comedian even shouted at him that He could prevent him but he didnt.

So simply, I preceded that Dr. Manhattan doesn't really care about people.

But like in the show when Sister Night tried to change the timeline by asking her grandpa a question in the past, that is how it all started, and Manhattan’s powers incorporated his own meddling as set in stone in the timeline

The “Before Watchmen” Doctor Manhattan prequel comic goes into the topic a bit.