Yes, but she will be a McConnell selection. They all are. Trump doesn't have a legal doctrine. McConnell does and has had for years.
Unless they select an idiot as a special master, this just slows things down slightly. But it also means Trump and his supporters can have no complaints that the courts are stacked against him. So it isn't all bad.
I doubt the DOJ will appeal, except if the Special Master makes decisions they can't live with. If Trump gets to keep a pen given to him by Kim Jong Un, who cares? If he has a privacy interest in medical records, so be it. The thing at issue for most people will be if he retained important secrets and failed to give them back after being asked. That should put him in jail unless the Florida judiciary is totally corrupt, which I suppose is possible.