Write an friendly, convincing e-mail to my landlord asking whether I can get a dog.
Dear Sir/Madam,

I hope this email finds you well.
I'm reaching out with a request regarding the property I rent from you. I'm interested in getting myself a dog and I noticed there wasn't a clause in our rental agreement specifying if this was allowed or not so I would like to consult you about that.
I work from home most days of the week and have a very laidback lifestyle, so I'm looking for a dog that can keep me company but also take me out of the house for walks. I'm looking into a small breed that is also calm and friendly - likely a french bulldog. They are easy to train and known for spending most of their day sleeping, this is also a very quiet breed that doesn't have a lot of complains of barking.
Is that something you would permit? 
I am also happy to hop on a call or meet in person to discuss further in case you have any follow-up questions.

Looking forward to hearing from you soon.

Kind regards