Can you use a hash as a password?
I'd say the key thing that you need to spell out to answer this question is this: 


What information does the attacker have?


This ties to one of the basic concepts of cryptography, called Kerckhoffs's principle: "A cryptosystem should be secure even if everything about the system, except the key, is public knowledge."  (I recommend you read that page and take its lessons to heart, along with the security through obscurity entry as well.)

So if we apply Kerckhoffs's principle to your proposal, we would assume that:


The attacker knows that your password is the hash of some secret word that you choose, but not which word;
The attacker knows which hash function you used to hash this word, and how to compute this hash function.


Then we trivially conclude that this isn't any safer than just using the word as the password.  And since "dog" is a very common word in the English language, it's an obvious one for an automated attacker to try.



I'd say that in your question you are doing something that most laypersons do when they propose password rules or schemes like this one: you're assuming that the attacker won't know or guess the rule you're using to generate your password.  But:


You just told your idea to the whole Internet.
Even if you hadn't, there's a good chance that an attacker might think of the same idea.


So really, the best passwords are random passwords, because there's no rule that an attacker can use to predict them.  



EDIT: Funnily enough, a few days before this question, Duo Labs published a security analysis of OEM PC software updaters (press release; PDF report), that contains this gem (p. 16):


  Unfortunately, the encryption utilized is RC4 with the pre-shared key “e8fded24af79202d7da48adefe4a3a04”, which is the MD5 hash for “Asus Live Update.” As this layer of encryption boils down to simple obfuscation that can be dealt with on the fly, it provides no security value.


This is almost perfectly analogous to the question's proposal: 


Pick a secret passphrase ("Asus Live Update");
Hash it with a standard hash function;
Use the resulting hash value as an encryption key.


And yet the researchers, just from seeing the hashed value, managed to guess the passphrase and the hash function used to obfuscate it.  So there we have it, a documented real-life failure of the strategy.