Cheers. I've tried out the demo. In general, the idea is pretty good and original, but at the moment the game is far too buggy to be enjoyable. I'll just post all my thoughts below.
Title screen and music are nice, and I like how the game starts. Intro cutscene is well made. How come the credits are right at the start though rather than at the end?
The cursor sound is kind of loud. The music is too. The music seems way too happy and upbeat, considering the cat and the dog are both depressed that they got lost and are stuck in the city in rainy weather. I'd imagine a slow and sad song would be better here.
Some of the dialogue is a bit strange and sometimes the characters talk too much, like early on. They just kept going on and on before I got a chance to so much as walk across the street. You might want to check the spelling and grammar too. I came across a fair few errors in that regard. Also the windowskin colour is a bit too bright, making white text a bit hard to read against it.
I also noticed that in the menu both Cat and Dog have a default 'Soldier' class. Might be a good idea to change that.

Will there be combat in the game at all? If not, then maybe HP and MP bars aren't needed either.
When I try to interact with tutorial signs, I have to be one tile away from them. Why not just make the interact event on the sign?
I also got this error. I've recorded it on the video. There are 2 errors actually. One is that there's no passability on anything (or maybe I was just set on Through), and the other is that Cat and Dog both got stuck facing the same direction. It's really weird.
Here is the video that I've recorded, because it's hard to explain it in words:
https://dl.dropboxusercontent.com/u/63155786/Cat%20and%20Dog%20error.wmv
I also think it'd be nice if the player could save anywhere. Not entirely sure why it's disabled.
When I reached the exit tutorial event, I got this:
"Would you like to finish or skip the rest of the tutorial?"
Choices: Yes and No.
Which of those does Yes refer to and which does No? Is Yes referring to finishing the tutorial or skipping it?
I also tried out the fishing mini-game in the park. I caught two fish the first time. Then I tried to play it again, but the mini-game just didn't happen. I was just transferred back to where I was, yet the 1 min time limit began ticking down for no reason.
The world map looks very nice though, and I like how there are so many places to visit. Really, this game looks like it has a lot of potential. The idea is great. But right now it's just too buggy and needs a lot of polish. I hope this feedback comes useful and that you continue working on the game.
