Do I still owe rent if I never moved in due to no fault of my own?

You can pay the rent. Unfortunately, the fact that the neighbor had a dog--unless this was a "no pets" building or it was represented in the lease that your neighbors had no dogs--is not sufficient grounds to break the lease. In the absence of a term or clause like that, the landlord had no obligation or duty to disclose the dog--it probably wouldn't even occur to the landlord to do so. Even the fact that the dog was barking incessently was not enough, since it was barking on one occasion--that's not sufficient to constitute violation of your right of quiet enjoyment. (See below.)

The landlord can hold you liable for the full term of the lease, until he manages to re-rent the space. He has to try to rerent it--make a good faith effort--but you are on the lease until someone else is, or the lease term runs out, whichever is sooner.

You can try to move things along by finding someone to take over from you, either as a sublet or as an assignment of the lease.

(In the future: if this happens, you need to move in; if the dog disturbs your quiet enjoyment of the premises, you can complain to the landlord, who needs to speak with the other tenant and do something about it; if nothing is done, you can then bring a lawsuit if necessary. However, you cannot simply break a lease when a dog barks on a walk through.)