My understanding is the honeymoon phase is when your pancreas is producing some insulin. This may not be enough so, even when you are going through the honeymoon phase, you may start to need insulin.
So, I guess your question is how long will your pancreas produce enough insulin to not need to inject any.
Unfortunately, everyone is different. Typically, (but not always) this period lasts longer the younger you are.
But, as it is not known what causes your body to start attacking the cells which produce insulin, there are no obvious ways to put off injecting. It may help eating a low carb diet as the less sugar you put into your body, the less insulin that is needed to convert it to energy. But this is not really prolonging the honeymoon; it is just reducing your insulin needs.
I understand the idea of having to inject multiple times a day for the rest of your life is not the sort of thing anyone sensible would look forward to. However, it is not the end of the world: there are many of us that do it and live very full lives. I guess if you had gestational diabetes during your pregnancy, you managed to achieve something amazing by giving birth to your son whilst you are injecting.
If I had the chance again, I would make the most of my honeymoon phase to learn as much as possible about diabetes so, when the permanent injections start, I could take off running and as comfortable as possible.