It is time to get a probate court involved and get a guardian appointed. It can be a quick process and as a guardian you can order the needed ID and make all living decisions for your brother. As far as transportation, the new nursing home may be able to supply the needed the medical personnel to make the transfer. Getting a judge involved is always helpful in these situations.
Having a photo ID is not a requirement to have a document notarized, but having sufficient proof for the notary that your brother is who he is claiming to be is required. Depending on the notary, he may be willing to accept other forms of ID, like a birth certificate, other photo ID, library card, etc. The nursing home would likely have a Medicare card for him, which may be enough. You may want to talk to a couple different notaries to see what they would want. But, like in my earlier answer, your brother still needs to have capacity to execute documents, whether or not he has a photo ID.