"Yo quiero caminar con mi perro."
Translation:I want to walk with my dog.
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.
I put " I like to walk with my dog " but it was marked wrong. Any ideas please?
It's best to use querer for either "to want" or "to love". I see that duo lists "to like" as a definition for it, so I'd imagine that's where some confusion came from. However, from what I know it's uncommon to use it as "to like". For reference: http://www.wordreference.com/es/en/translation.asp?spen=querer
If you want to use it as "to love/like", a personal a is required. For example, I love my mother would be "Quiero a mi madre". If you are yet to learn this: https://www.youtube.com/watch?v=JPNWu61BAtQ.
Any further questions, reply to this and I will get back to you
Apparently someone entered "I would like to walk with my dog" as an accepted translation, so that's what you got there. I'm not a fan of it, though. "Quiero" is "I want", and "Me gustaría" would be "I'd like".
They must have listened to you, because I wrote the same and it didn't work.