The short answer is yes - getting insurance is likely a very good idea for your business. Incorporating your business can reduce the liability to you personally (so that if something goes wrong, people with a claim on the business' assets can't come after you for your personal assets). However, incorporating does nothing to protect your business from risk. That's where insurance comes in. There are several types of insurance that are relevant for small businesses (including general liability insurance, worker's compensation insurance, and product liability insurance). The type that is most relevant for you at this point is likely some form of liability insurance. This is important because when you're taking care of children, there are all manner of dangers you need to protect the children from -- if you should fail (god forbid), the financial ramifications could be enormous.
The good news is that small business insurance is often quite affordable, and can be set up within a pretty short period of time once you pick a company. A quick google search for "small business liability insurance" or something similar should get you on the right path. Another good way to find an insurance company for your business is to ask other similar businesses (yes, competitors) who their insurance company is. This helps because an insurance company that is familiar with your industry is likely to give you a better insurance rate (because they understand your industry, insuring you is less risky for them).