The image of Laura's doppelganger (in ep.29) and the image of the woman,who looks like Laura(in Cooper's dream) are one and the same,yeah.

And about the backward talking,I don't think it shows someone is a Doppelganger.Everyone in the lodge speaks backwards(except Cooper).I think that this girl in Cooper's dream(with the vision of Laura) is a projection of the lodge,just as Windom Earle,Annie and Caroline,we see in ep.29.they speak backwards,too,but this doesn't mean they are Doppelgangers.

Beware of BOB

When I call out no one can hear me,when I whisper he thinks the message is for him only..my little voice inside my throat,I always think there must be something that I've done or something I can do...But no one no one comes to help,he says,a little girl like you...

Online-Inquirer

Well......I think the Doppelgangers we see in the lodge are the following : Laura's doppelganger,Leland's,LMFAP's and at the end-Cooper's,although we see Caroline's white eyes,I don't think it was her Doppelganger....just a lodge presentation,in order to confuse Cooper and to make him weak...

 Everything is a big MESS...

Beware of BOB

When I call out no one can hear me,when I whisper he thinks the message is for him only..my little voice inside my throat,I always think there must be something that I've done or something I can do...But no one no one comes to help,he says,a little girl like you...

I must say that I agree with Ivalinda on this one. The girl in Coopers dream is Laura. Laura wrote about this dream in her diary -the page that Donna read. She wanted to tell "the old man" about Bob -"but my words came out slow and odd". That clears up the backwards talking. So. No dobbleganger. It´s Laura! Finito! She wanted to give Cooper clues.

Ditte

I agree with Ivalinda and Ditte.  Plus, another thing to add to this is that when Cooper says "Laura and I had the same dream".  She is supposed to have this dream (according to her diary) just a couple of days before she dies, BUT I think it is also the same dream that she has in FWWM, with the painting etc.  True, this is not the same scene, but considering Coop and LMFAP are also in it, I think it has to be the same dream, just maybe a longer version of it. 

I also don't think the Laura in the original (episode 2) dream is Lauara's doppelganger, but a premonition of Maddy.  I don't think it's necessarily a premonition Maddy will be the next victim, maybe just telling a way of Coop's subconscious telling him Maddy will soon be there as well as giving him clues about Laura's murder.

I think in the final episode we DO see the doppelgangers of Laura, Leland, Maddy, Caroline and LMFAP, all characterised by their white eyes... 

"watch out for my cousin.."