Most episodes have no narrator, so no, the term "unreliable narrator" doesn't apply.
A more useful way of looking at what you're asking is probably What is the perspective of Bluey? Is it more subjective or objective? And what are the rules of the Bluey universe?
Asking those questions together you'll find that these vary from episode to episode; however, I find that one of the appealing things about the show is that maybe the xylophone is really magical? Maybe Bandit would have stayed with a hose in his mouth forever? The Heeler family fully commit. That's the magic of the show. We are mostly in the kids' perspective, but because of the adults' full commitment to the games then that perspective becomes the reality of the show. Different to our reality, hence why you find it 'unreliable', but consistent for the show.
That being said, not all episodes have this sort of 'magical realism'. Sometimes the parents are reluctant, or something gets in the way of them playing the game. Other times, the perspective shifts, like in S1 E37 "The Adventure", where Chloe and Bingo switch roles for various reasons. The music pauses whenever they are out of character, then restarts again. Here, the show breaks it's own illusion, but then manages to recreate it - you can follow the story of the adventure even though the 'actors' playing the roles keep switching in and out. In these sorts of episodes, it is obviously just a game.
But whether the show is flirting with magical realism or not, I don't think the concept of an unreliable narrator really applies to what the show is doing.