Diabetes mellitus

My thirteen-year-old girl just got diagnosed with Diabetes Mellitus. My vet also said she appeared to be in the early stages of Diabetes Ketoacidosis; they saw ketos in her urine. She also has a UTI. They did not want to hospitalize her so they gave her fluids and a few shots (a 2-week antibiotic and for nausea as she hasn't been eating well for a few days). They appeared pretty hopeful that getting her on insulin and balanced out is very possible. They sent me home with canned food and she did voraciously eat it about an hour after we got home. She did receive an insulin shot when we were at the vet and they showed me how to administer the shot. She needs 3 units of insulin twice a day. She's a Chihuahua mix. I was too anxious when at the vet to ask many questions. I lost my Father at the end of September and just last night one of my parents-in-laws had a very good boy (also thirteen) pass away; I'm pretty emotional right now and too scared to ask in person ...

Realistically, how long will a thirteen-year-old dog last after such a diagnosis? Am I being too much of a worry wort or will this significantly impact her quality of life? Is there really hope that she can stabilize and have a few good years left in her? With minimal suffering? Or would I just be prolonging her suffering and the inevitable?

I'm admittedly having a really hard time right now, so please be as gentle in your opinions if you can but also be real with me. I adore my veterinary clinic but I wonder if their optimism might be played up