The idea of humans being gods is good, but I think a lot will also depend on how/why humans disappeared and what the dogs know about it. I mean, it's a very different story if humans died (and their bodies were laying around being eaten by cats) than if they just vanished one day. You also have to figure that there would be a tremendous die-off of dogs, especially pedigree dogs. All those "super cute" cosmetic breeds that humans have developed almost certainly died out pretty fast. The circumstances around the human disappearance will have an impact on how it is understood and remembered by the dogs.
On a related note, depending on how people disappeared and what happened immediately after that, you might lose most dogs who know anything about people. I mean, most dogs that live with people live inside, and if there are suddenly no people to open the door, those dogs might never make it out of the house. That could mean that human worship is a sort of fringe religion among the few survivors who actually did live with people. That would be a great source of conflict if you paint the house dogs as a fanatic sect largely discredited or possibly feared by the rest of the dogs.
What you could also do, if you want human-worship to be more wide-spread, is to make those few surviving house dogs almost oracles. Obviously, in a post-human world, many of our inventions and contraptions are still around, and after only three years, most of them would still be in play. Things like grocery stores might still be mostly intact (again, depending on the nature of the human disappearance), so dogs who have been into those stores with people in the past might know how to get inside, or where to find food in them. Maybe dogs who used to live in houses know that food comes in cans, even though you can't smell it. Service dogs would know how to open all kinds of doors too, and flip switches and do all kinds of "magic" things with these human artifacts.
If you don't want dog religion to be that human-centric, dog religion would probably reflect human religions in many ways. For example, their deities would likely be canine. Just as humans had the fey, dogs might view wild canines like wolves and foxes as semi-divine creatures. Because dogs are pack animals generally living in family groups, they are well-suited to a familial pantheon featuring different gods in different roles. For example, the father deity who protects and punishes, the mother deity who cares and provides, the sibling deities who get up to mischief and create many of the stories and legends that will be told. Only three years after humans, this kind of established religion would probably have to have come from wolves or coyotes or something.
What might be interesting to look at would be different pantheons for different breeds. Generally, people have gods that look like them, whatever that means to them. It might be just have a human shape, or it might have the same skin color, or it might have the same oblong heads, but people usually make their gods look like them (there are, of course, exceptions). With so many sizes and styles of dog, whether or not you choose to go with a human-centric religion or not, there is fertile ground for breedism. For example, if humans are gods, surely the Pomeranian is more divine than the husky because humans put so much more effort into Pomeranians. That also means that the dogs who would be most devoted to the Divine Human sect are likely also dogs who have the most to gain from it. After all, a pedigree dog could claim superiority through breeding while a former stray might rebel against a faith that makes them second-class citizens. Alternatively, if you broadly adopt a wolf religion that has nothing to do with humans, human-altered breeds would either be no different or would be scorned.
Whatever you decide, remember that religion is a practical concern. It serves a purpose, often an emotional one, and creates a sense of understanding of the world and the practitioner's place in it. If a pack lives in an area with severe weather, their gods are likely to be temperamental and strict. If they live in a fertile and safe area, their gods are likely to be generous and kindly. The issues that the pack faces will determine what they need from their religion, and so will change what they believe and how they practice or express it.