Convince my mom to let me get a puppy..?

ok im 17 years old, and i have had a job since the day i turned 16 and have nvr been fired. I have recently seen a dog i wanted and i have been saving for awhile. I ve made a list of all the expenses ill need and i have been buying things here n there so i wont have to all at once. My gf makes 300 a week so i know well have money for it. The only problem is itll b in my moms house and i plan on moving out in little while. My mom will not say Yes to the dog. How do i convince her?