"Hello! Veterinarian", it's not specifically a dog manhwa but it's totally about animals
I don't know that many dog manga, but I can recommend a few cute pet manga to you. I hope that helps a little.
https://www.mangago.me/read-manga/ame_to_kimi_to/ (woman adopts a tanuki)
https://www.mangago.me/read-manga/encounter_between_polar_opposites_and_their_dogs/ (a man and a woman with their dogs )
https://www.mangago.me/read-manga/hiroware_koneko_to_moto_yakuza/ (Yakuza who adopts a cat)
https://www.mangago.me/read-manga/emperor_to_issho/ (highschool girl keeps a penguins as her pet)
Oh and this is also cute:
https://www.mangago.me/read-manga/kujima_utaeba_ie_hororo/ (It's about a guy who meets a strange bird and lets it live with him and his family )
Sorry for your loss TwT not pet-related, but I find this one super wholesome: https://www.mangago.me/read-manga/t_sensei/
And this one hasn’t cute birds: https://www.mangago.me/read-manga/southern_bird_and_northern_bird/
Has* cute birds (●'◡'●)ﾉ
Thank you guys very much ! I appreciate it
It would be nice if it was something wholesome