Depending on your definition of "dog-sized", there already exist bats that large. Various subspecies of the giant flying fox already have a wingspan over 1.5 meters, albeit with a mass of less than two kilograms.
For my answer, I'm going to assume you meant something substantially larger than what already exists out there, perhaps double the wingspan. I'll be outlining some major points for consideration, and suggesting likely changes.
Diet: Most bats are insectivores, but those are small. I strongly doubt that a diet of primarily insects will be dense enough in energy and nutrients if you scale your bats up. I suspect your bats will mostly be hunting small animals, but fishing or eating fruit are also possibilities to provide other options. Bear in mind that bats eat about their own body weight's worth of food daily: these are going to be some very hungry creatures.
It's good news for you, then, that all of those already do occur in bats; not necessarily all in a single specimen, but bats have a surprisingly wide variety in their diet. Most of the larger bats, like the flying foxes, have a diet composed primarily of fruit. Certain bats with specialized adaptations regularly target fish and crabs or frogs. The noctule bat can even hunt birds as they fly! Making your bat larger will probably not do it any harm with such prey, although a dense forest would be more problematic; still, you can plausibly have your giant bat attacking rabbits and birds readily enough.
Flight: This amounts to checking if a wide-winged bat could still fly, and I believe it could. You might lose some maneuverability in raising the wingspan so high, but bat wings have a great deal more flexibility than bird wings; they can probably compensate for that loss. There are birds with wingspans of 3 meters or more, and they can fly; bats can't glide as well as birds do, but I see no reason why a bat of similar size can't fly for shorter periods. Bat wings do tear easily, so bear that in mind: they heal quickly from small tears, but they can't afford to get caught in an actual fight with their prey.
Temperature: This is probably your biggest concern. Bat wings have a tremendous surface area for their size (basically a requirement for flight-capable wings); this is great for shedding heat, but it has drawbacks as well. With that much surface area, they are extremely vulnerable to low temperatures, and bat wings can't naturally grow any insulating hair over most of their surface to try and compensate. Eating huge quantities of food could make up for such heat loss at the cost of needing to be capable of hunting that much, but it's still a huge disadvantage. I wouldn't expect your giant bats to fare well outside the tropics, but that is a constraint on your bats, not a denial of their ability to exist.
Predation: The giant flying fox has eagles and giant snakes as its known predators (not counting humans). From your description, large birds aren't present, and it's not exactly going to shatter your reader's suspension of disbelief if you posit that this area of your world doesn't have snakes in the four-meter-plus range. Even ignoring that mundane solution, if your bats are double the size, they're going to be much less tempting as targets.
Conclusion: Reading up showed me that there was a lot less to change than I first thought. Most of what you're looking for is already present in bats, and your world's extinction event has apparently cleared out any larger competition. I don't think you'll get pack hunting without a lot more changes, because they don't need that for anything they're going to be targeting, but with your world as stated giant flying foxes are already basically apex predators: make them larger, give them an adaptation to hunt small animals, and you're as good as done. Really, it seems like your biggest concern is why the bats even need to get larger at all: perhaps it's to keep off potential predators?
