A dog is a lot of work and money. They need to be fed and walked three times a day. They need to be washed, they need regular trips to the vet. You are probably in school, you have exams, you have sports meetings. Your mom is thinking that she will be the one to take care of the dog. So to finally answer your question. Do you have time to do a side job to buy food for your dog? To save some money when lassie gets sick and needs the vet? Will you always have time to give your dog the attention it deserves?
Start doing chores around the house with out being asked or told to. Do your home work as soon as you get home with out being told to. You can also try and do some research on different types of dogs to see what breed suits our family's lifestyle.
Ask her what she thinks would prove your responsibility. It'll probably be stuff like cleaning your room, taking out the garbage, doing the dishes, you know, CHORES. Then, just start doing them on your own WITHOUT being told to. She's not gonna say yes overnight, but I guarantee she'll notice. Then you start planting the puppy seeds. Dogs do cost money though, and it's not all fun and games. I just got done walking my 2 dogs, and it's 40 something degrees outside and raining. Cold+Wet.
start doing things you normally wouldn't do make your bed do chores 4 her ask to do the groceries that works 4 me and i have a dog what kind are u looking into getting i recommend dachshunds they r amazing