My doctor said my x-rays showed that a vertebra in my low back is slipping forward. Will this get worse and will my spine eventually slip off?

Possibly. This may stay the same for many years though most likely it will slowly progress over a long period of time. Whether or not it will be symptomatic is hard to predict. The technical term is spondylolisthesis that you can search for on the web. The good news is that there are very good treatments for it.
Spondylolisthesis. It literally translates to mean a spine bone slipping . Think of the spine as a stack of a child's abc blocks being perfectly aligned in a tower formation and then pushing one a little over another in any direction and that displacement is what a spondylolisthesis is in the spine with one bone slipped or displaced over another. There are several different types. They rarely progress at all.