You are welcome to borrow a guitar of mine for the lessons at any time. However, you wouldn’t be able to take it home to practice, so wouldn’t get good value from the lessons. It could make sense to try a single lesson first to see what it’s like, and then purchase the guitar afterwards. I also don’t have any children’s sized guitars, but we could often use a small-bodied full size one, or even just play a ukulele.
Once you are ready to buy a guitar, feel free to chat with me about what you would like. If you are a beginner, you can see some suggestions on guitars you might want to purchase here.