This law is consistent with the Heller decision because it will allow people to keep loaded and functional firearms on their person, within their immediate control, or within a rapid-access locked container. The Washington DC law found to be unconstitutional by Heller didn't allow those things.
I think the Heller decision would be relevant because the poor cannot afford rapid-access containers, and the highest rates of crime are certainly in the poorest areas of any municipality.
According to the U.S. Bureau of Justice Statistics (https://www.ncjrs.gov/pdffiles1/bjs/104274.pdf,), 89% of men and 73% of women will experience at least one violent crime during their lifetime. That statistic alone justifies having a self-defence weapon readily available, not locked up in some safe or closet.