I am so sorry. i was a similar age when my first dog died.
When i was 13 my dog who was also 13 (parents got her when i was 1) became very poorly and had to be put to sleep. It was very traumatic for all of is and afterwards we all went away for a few days to the country to mourn. We spoke about all her funny ways and gave ourselves treats.
When we returned we spoke about getting another dog and after a few months we did. She never replaced the first one (especially not for me as the 1st dog had been more like a sibling) but we loved her just as much.
Then when she became poorly 9 years later (with cancer) she continued to live a happy life for 2 more years with medication. At the end she let us know it was time to have her put to sleep - she dug a hole under the apple tree and lay in it.
I returned from uni to be with her and my parents and the vet came out to the house. It was very peaceful.
My parents kept me informed all the way through both experiences and i felt involved in the decisions. It helped me say goodbye to them and learn how to cope with loss.
Of course it hurts but that just shows how much you love them. The depth of the grief is balanced by the amount of joy they give us.
I know these seem like trite platitudes but time does heal and death is an integral part of life.
I hope your dd will grow up with happy memories of her life and accept her death. I feel that we have a responsibility to give our animals happy and fulfilled lives and if we have done that then that is the best we can do.
Good luck with everything. xx