Agree, it's possible a cat would fulfill whatever it is that OP is looking for from dog ownership. I don't remember her actually mentioning what exactly that is, only that she's been dreaming of getting a Labrador puppy forever, so it's hard to make informed suggestions based only on that. The suggestions of an older, smaller, calmer, trained, vaccinated dog would also seem to make some sense.
I know my suggestion of rats would have probably also been instantly written off by the majority… I'm aware it might sound kind of left-field to those who aren't familiar with pet rats, and it's possible that rats wouldn't work for OP.
But when the pet somebody is thinking about getting (but for practical reasons, reluctantly decides they currently shouldn't) is a dog, then compared to a cat, the experiential quality of looking after, interacting with, and building a relationship with pet rats is IMO closer to the specific flavour of animal companionship you get from a dog. Obviously keeping rats isn't the same thing as having a dog, but I don't think it's as different from dogs as the way you look after, interact with, and build a relationship with a cat is.
If what somebody is looking for when they're thinking of getting a dog is an animal that's friendly, intelligent, responsive to you, always glad to see you, playful (except middle-aged+ male rats, who mostly want to chill), (somewhat) trainable, and that relates to you in a kinda dog-like way and thinks in a way that's kinda familiar to humans (if less complex), rats might be a good choice. (Always worth mentioning you shouldn't just have one lone rat; they're social and intelligent, and you're incapable of some kind of rat interaction, so they need rat companions.)
Lots of people obviously love having pet cats, but depending on what OP is looking for from dog ownership, cats may be too fundamentally different an animal from a dog.
The natural social structure of rat family and friend/acquaintance groups, the rat ecological niche and strategy, and the way that rats think and behave, is extremely similar to humans, just closer to the ground, with more tail and less brainpower. Like us, they naturally build complex networks of relationships, and they tend to treat their owners… not quite as another rat, exactly, but as a sort of giant friend, someone who's always worth spending time with.
Dogs also live in fair-sized social groups, and of course have developed specific behavioural tendencies towards building relationships with humans that have a particular quality about them. Rats and dogs aren't anything like identical in how they relate to humans, but they're not completely different.
The relationships cats build with their owners and vice versa are of a type that do feel pretty different from that, IME. That's no less rewarding, of course, for those looking for that kind of interaction and relationship, but because of the natural differences in the way cats interact socially and build relationships, their way of life, ecological niche and their psychology, they're a really different pet.
Also, if you really really need to go for walks, you can (if you like) go for a walk with a rat on your shoulder, pirate-style, or in a hoodie pouch. Just saying
As long as you're mindful of the fact that small animals have small digestive tracts, and can't hold on forever…
Anyway… OP probably has a lot of different options for pets that she could provide a wonderful life to, without massively disrupting her life, but if what she actually wants is specifically and solely to have a Labrador from puppyhood onwards, maybe settling for an alternative wouldn't be the best thing. It wouldn't be what OP really wants, and that could end up being a really difficult situation.