R.,
One thing that might help her understand (slightly!) is that Dusty 'hurts' - if he is in pain(?) - and that the vet can't make him feel better. Explain that he is very, very old and doesn't feel well. Try to avoid saying anything related to sleep, as I have heard this can cause anxiety over going to sleep, seeing people or other pets sleeping, etc. She isn't going to understand everything, but she will notice he is gone and know that you have told her that he was not feeling well, couldn't get better and was very old. You have lots of wonderful memories to keep with you. Our vet did a paw print ornament type thing that we picked up a few days later and we keep it by her pictures. Make a nice scrapbook page and talk about how wonderful he was :-)
When my daughter was almost 3 we had to put our 16 yr old dog down as well. She went with us to the vet and sat with us when Cocoa was euthanized. We distracted her during the shot so she didnt negatively associate that with death. Overall, it was a good experience for her. She saw that we have emotions and loved our dog, and that we were there for each other. She still talks about her and says she misses her. We keep pictures and talk about her.
I am sorry for your loss and situation.... if only they could be with us forever :-(
Best wishes...