Your mom is right. You should wait until you're older.
If you still want to get your eyebrows done, then I suggest you find a friend who has nice eyebrows and ask which location they visit. Also ask about the price and make sure your mom is okay with it.
Since it's your first time with threading/waxing/plucking, you might want to bring in a picture so the stylist has an idea of what you're looking for in terms of thickness and arch of your brows. If you like the results, then always go back to the same person.
Be warned: There are a lot of people who are not good at doing eyebrows. Either the stylist does a good job or they really mess it up. It takes a long time for the hair to grow back.
And yes, doing your eyebrows in the morning can be very time-consuming.