Yes, you are right. Google is a search engine and you can use it to your advantage to very quickly find out what the copyright status of an image is. There is also Tineye, which you can use to double check an image you have found.
It’s a great idea to think about a sharing for photographers, but still permission from the original photographer would always be required, because some images have restrictions set on them. For example, there are images that are restricted to use in certain territories, and there are restrictions on using images with people in them unless they have signed model releases. Even then, there are restrictions agreed upon in the model release!