Let's take a quick look at the costs involved with DIY-ing this project instead of hiring a professional to install your stove:
You'll save on labor. You can save a little money on the upfront cost of installing a wood-burning stove by doing it yourself. For example, you won't have to deal with labor costs. This could save you hundreds or even thousands of dollars.
You'll still need to pay for materials. This includes the stove, venting, and more. And if you want to put in a chimney, you'll likely need specific equipment that you might not have in your standard toolkit — not to mention a tall ladder. It might not make financial sense to invest in these tools if you're only going to use them once.
You'll pay for mistakes. Be honest with yourself about your skills and limitations. There could be real (and expensive) repercussions if you don't install the stove correctly.
You'll have to navigate permitting fees on your own. The permitting process can often be difficult to navigate, especially if this is your first time dealing with the local bureaucracy. But local professionals deal with this all the time. They know how to fast-track projects so they're not stuck in approval limbo forever. If your project has to go on hold for three months while you're waiting for permit approval because you filled out a form wrong, that delay may cost you even more.