Converting DBA to LLC
What you are looking for is actually reorganizing your business as a Limited Liability Company. First step would be forming a Missouri LLC, and then second step would be reassigning all the business assets (such as your truck) and all the contracts from your sole proprietorship to this LLC.
I am not sure how the process of reassigning assets works in Missouri, for that I would recommend you to consult a business attorney licensed to practice law in Missouri.
Keep in mind though, you can only use the name "New Life Landscaping Tree Service & Hauling, LLC" after you have the LLC registered with the secretary of State. You do not gain limited liability by just putting those words in your company name.