Your mom's not loosing a son or a daughter, her son is simply changing his body; what does she truly value about keeping a son, is she one of those 1745 parents who care about passing down the lineage with heirs? What, does she think if you stay a boy, that you're suddenly going to go out and play football and do "son" stuff? If you're still living, she's not loosing anything (and if she looses your relationship with her, it's only her fault). While I know you want to keep a relationship with your mother, sooner or later you have to put the foot down and explain the situation like it is; she needs to know that no amount of religious or tradition views override love and acceptance, and that if she can't accept that, the relationship probably needs to be cut off before it causes more pain.
Also, it sounds to me like you've put all your stress and emotions into your relationship with your dog, which to be honest, is probably the direct result of not having close friends in your life; it sounds like you've been hurt a lot socially and would rather keep indoors and keep company with your pets rather than people. It sounds like a lot of this has manifested into the pet, and while it's always hurtful to loose a pet to death or moving, it sounds like it's the actual loss of the relationship and physical contact with the dog that upsets you. For physical contact, company, and conversation, a relationship with another person truly is the most rewarding. I don't mean to sound rude with this at all, but primarily depending on a pet for these things for too long and too strongly can sometimes lead to a person becoming romantically or sexually attached to the animal. While I can't discriminate against people who are married to their pets and such, sexual bestiality is still plain against the law, and all that....basically, long story short, I'd just say it sounds like you'd really benefit from finding a special way to socialize and meet others.
If your friends in your social life have reacted badly to your transition as well (or just if no one's ever liked you period), always make sure to improve your physical appearance as much as possible, always make sure to participate in the careers and activities you enjoy the most, and simply make sure you're the most confident "you" you can be, no matter what it takes. If people see you in a confident, attractive, well-kept state, they automatically sense you're the coolest person around and realize that they either need to respect you or take a hike. While being a woman is usually about being softer and submissive, you still have to beam with confidence and a grown attitude, or else people will see you as the "I can walk all over them" person. That type of position can lead to depression very quickly!
