In English, we usually say 'I want to walk my dog'. can you use a similar construction in Spanish, or must it always be 'with my dog'?
The usual expression for walking your dog is "pasear al perro", pasear itself meaning "to take a walk, to stroll". Using "caminar con" with this meaning is also possible but a bit rarer.
Also, andar al perro works.
If my dog is a female, would it be "mi perra?"
If you want to explicitly state that your dog is female, then yes. If your dog's gender is not important, then use "mi perro", which is the general case.
When I wrote this I meant "I want to walk with my dog". I think there is a difference between saying that and saying "I want to walk my dog". My goal is to walk and take my dog along with me.
Because quiero means want. Not like.
I left off the "yo" and this was marked incorrect. How do I know when I need the subject to be stated and when it can be left off?