Well, I must say CGJ, I am impressed. I must admit though, when I first saw this thread, I was like, uh oh, whats going on this time. But having read through it all, it seems like you're actually getting somewhere. So as a prize for your efforts, I am willing to offer you some of my (most amazingly professional) advice.
First off, instead of applying for beta testers, just post latest updates of the game, so we can all continue to test it. I mean, I downloaded the 1 posted right at the start, and thought: "Meh, its ok, I guess." But seeing some of your images, I want to see what it is like now.
Second of all, in the version I downloaded, I noticed that only part of your house was actually showing, but the background image was somewhat larger. This leads me to believe you have the resolution set wrong for that background. (E.G. you probably have it set to 640x480 and the background size is 800x600.) My advice on this, would be to look for some way to change the resolution. (I know how to do it in Dark BASIC Pro, but not Dark BASIC Classic.)
Third of all, if this is going to be anything like having a real dog, you will need first of all, a series of psuedo-random actions for the dog, such as it randomly peeing on the floor because it isn't house-trained. Then once you have this, you need what most AI based games have, the "good doggie gosub" and the "bad doggie gosub". So you'll need some way to let the dog know, and keep stored, what is good, and what is bad, so it either, continues doing something, or stops doing something. (Examples of this are in Black and White (& 2), Creatures (2 & 3D) & the Neichize 3D pets series.
Fourth of all, you need some collisions, to make the game a bit more interesting than simply some sprites on a background image. I personally choose 3D above 2D, so I'm not the most experienced in sprites, but ask/search around for methods of sprite collisions and how to get complex sprite collisions (for things like walls, curves etc...)
I hope some of this was of help, I also hope to play a newer version of this game, and finally I hope that this does become a finalized release on your behalf.
Well done.