I think the conventional answer is “no dogs do not have a soul so they are unable to go to heaven”, even Rudgard Kipling in his wonderful poem Dinah in Heaven seems to accept there is no place in heaven for dogs other than Dinah, to even pose this question pre-supposes there is a heaven and if there is a heaven is there purgatory and hell. I have a very simple, perhaps even naive, faith that there is a God, despite the agnostics and atheists having the best arguments, but I do believe there is a God and this God would not have a purgatory or hell and would certainly let dogs into heaven.
I see no reason why dogs and cats should not go to some sort of afterlife, whatever each of us believes in as individuals. I certainly found that thought comforting in the past when my dear cats passed on.
I am not a spiritual person but I do believe that there must be something better in the afterlife. Everything in life birth birth in animals and lots more things are so detailed in everything. This can be discussed for evermore so we just have to believe what we ourselves believe and hope.
I'm afraid I'm one of those that doesn't believe in the after world but if by some chance I'm wrong and I end up there I wouldn't want to stop without my dogs.