Great idea for a game. The pixel art is cute and it's fun to see how the monsters react to your choices.
I think that the wait times on unlocking abilities really mess with the puzzle aspect of the game. I'd much prefer if they were leveled up based on your accomplishments studying different monsters instead. For example: You interact with the cat with your basic commands to get it into several different moods, for now you don't have the tools to get it into every possible mood. Your research on the cat unlocks the Harpy, you interact with it and it unlocks a new type of tool. You use it on the cat and it puts it in a new mood, which unlocks the snake and so on.
I just don't think that idle games mash well with puzzles. It's like if you have to solve 2+2, but to unlock "4" you must grind your math skill for 20 minutes.
I do think that the concept is really good, but the gameplay needs to be re-imagined a bit.