Can you put aside 50$ EVERY month? Then by all means go buy a yorkie!
It will need shots when you get it, it's teeth done at 1 year old, then you'll need money for shots every second year, teeth cleaning, emergencies etc etc.
So look at your budget and if you can't fit 50$ a month in a savings account, then wait till you can.
You sound very responsible and I am glad you'll take full responsibility - I am sure you will make the right decision!