Its always sad to see a pet go, they wiggle their little bodies straight into our hearts, and connect to us a lot closer than most of the people we call family. All I can say is that you have to cherish what you had with your little puppy, because the strongest of memories never fade away if they are tied to strong emotions.

I lost my pet cat Tigger when I was very young. He would always snuggle up to me and my mother whenever we were sad. I missed him too! @UltimateGhost3 said it best about strongest memories being tied to strongest emotions.

It's sad...

but you might get a new pet that's a re-incarnate of Trixie.

It's never easy, loosing a loved one. I've had to go through it a number of times. But the pain of loss, is worth each day of love, comfort, loyalty and kindness they've shared with us. 

You've made her 13 years the best she's ever had. Never forget the good you've done. You made a huge difference in her life. 

Aww, Mesme, I’m sorry. *tighthugs*