((((((((( Blue Sky )))))))))
Birds represent desired goals, your hopes and freedom of.
Keeping in mind that that dreams are your subconscious communicating with you. ..
Now I do believe that dreams are sometimes mixed up disjointed pieces of information, like a jigsaw tossed around... explains why other random events may be going on not directly related to your bird
This dream is pretty much communicating that your afraid that you may be disappointed should some outside influence disrupt the path towards your aspirations.
Perhaps you think some gossip or crap talk could bring on this disappointment.
You do acknowledge that help is available if you need it ( the vet ).. but it still nags at you that something might go wrong.
I love that you saved 'random" bird.. tells me in your heart you know you will protect someone else's aspirations also.. ( help a friend reach her goal )
friendly dogs oft represent friends or companions.. perhaps you were afraid at the time that a friend might not be so encouraging for you to reach your goal.. ( or become/ do what you hope )

you did get your bird back.. Your pretty determined.. good for you
Kidnapped to Canada.. skip to a new thought here..
Finding yourself out of place against your will.
naturally the thought of your bird followed though in your subconscious and was probably playing on your mind at the same time with other thought pattern popped in.. ( hope that makes sense )
.........
In real life I did have one of my dogs take my beautiful cockatiel.. if i does happen dont change your dog.. mine swallowed him when he got cornered just so I couldn't get what he had.. my dog i a real smart azz.. he knew he did wrong.. my other dog was dobbing him in too..
i looked up from what I was doing because my other dog was jumping at me, I was just in time to see him grab him the moment he tried to take flight..
I have never clipped my birds wings since..
lol.. my rainbow lorakeet even got out once and spent the day with a wild flock....
he came home at the same time my husbands car pulled up after work.. he was exhausted!.. he is not too keen to do it again..