I am sorry to hear about the loss of your pet, Geoff. You need time to get over your loss, getting a new dog so soon is the wrong idea. The new dog can't replace the other one. You parents need to understand that people do grieve when they lose a pet. I cried for days when my cat died, and I still cry today, 8 years later. That's how much it hurts.
Try to tell your parents how you feel, make them understand, and let them now that you are not ready for another pet right now.
I hope it goes well.
*hugs* Kylie