Yes, if it is your first interaction with the neighbor, it will be seen as weird. The neighbor will feel judged, like you're saying the dog is inadequately cared for now. They may worry that you have bad plans for the dog as well. Plus, how would you access the dog in the middle of the day to play with it or walk it? With a key to their apartment, something I would never trust to someone I just met.
So you need to meet this neighbor first and then, if their dog appears to like you and you appear to like the dog, it may come around to you saying that there are times you wish you had a dog so you could go out for a walk with it during the day, and that walking by yourself is not the same, and them saying well hey you can always walk [DogName] I suppose and you saying oh my gosh really that would actually be a ton of fun I want to, and eventually working out the logistics of it.
But now you have a problem - how do you meet a neighbor you don't know at all, not even to recognize in the elevator? When you don't know anyone in the building? Be creative. For example, host a small party and invite only the apartments that surround you - next door on each side, across the hall, below you, and above you, for example. Call it a "meeting the neighbours" party and be clear you're not inviting the whole building. Sign it "RealName in ApartmentNumber". When people arrive, give them name stickers and encourage them to put their name and apartment number on them. Ask people things like where they work, do they have kids, a pet, whatever. Trade ideas about neighbourhood services and shops. Make some friends. Now when you see someone in the hall, you know it's Steve from 3B. Or the person in the elevator is Ellen from 4A. This is good even if the dog thing goes nowhere.
If it turns out that the person who lives above you is horrible, you don't ever have to talk to them again after the party. But this might open the door to you spending some time with their dog. (They won't bring the dog to the party, so this is just step 1 of many steps, be patient.) It might also turn out that the people below you also have a dog that you just never heard, or that the people across from you have a salt water fish tank. Who knows?