There are as many different opinions for interpretation of dreams as there are people that do it. It depends on who you ask.
The mechanism of why we dream is not fully understood - by anyone. That it is a function of the sub-conscious is fairly well agreed upon but there are many theories as to why and how we dream.
People have different solutions with the conscious mind when presented with the same data, it is far more difficult to explain the functioning of the unconscious one.
It is, however, a practical certainty that there is no pre-cognition involved.
A different response:
This dream might be a play on words, related to the expression "being dogged by a problem." There is some issue in real life that just won't go away - it keeps "dogging" you, following on your heels like a hound that won't give up. In the dream, stop running, turn around and face the dog. In real life, the solution is to figure out what the issue is, then stop avoiding or running away from it.
It means " Fat Basset Hound " ( a basset hound is a type of dog ) and the word Davidson comes from France, therefore the basset it from France.
Dwarf
This might be your subconscious mind's humorous comment on your dog's smelly habits. Alternatively, it might relate to recent terrorist bombings and the need to "sniff out" information like a hound.
chasing your dreams means pursuing a dream, doing what it takes to acheive it, being determined and really wanting to achieve it. :)
When anything is chasing you in a dream it usually means that you are under some stress in work, school, or relationships.
it means you should buy a hippo
From the phrasing of the question, this sounds like a one-way affection. The dream illustrates the uselessness of chasing after someone who does not feel the same attraction.
Your "Princess and the Frog". Love, Oliver
it means hamsters hate you
It means you need to run faster.
Maybe you need to lay off the unhealthy foods...
A dream animal of any sort doesn't really exist, so if you're chasing one, you're off on a fruitless quest. In America, we say "off on a wild goose chase."