When is the best time to tell an elder with early moderate dementia that she is moving to a nursing home?

There's no good time. Its a sensitive topic. Try to make her feel she is part of the decision making, rather than being 'forced.' Check out potential senior homes alone first, then take her along once you've found a nice one. Avoid the word "nursing home" as it has negative connotations of "institutions." Talk about senior living, with apartment-style accomodations, and activities with others her age. Your mom has to warm to the idea, so don't expect her to be on board immediately. In the long run, its best for her safety and well-being.