Katillac

Flat out no, there is no case for abandonment here. You worked your scheduled shift then reported off to a nurse who accepted the assignment. It doesn't matter what your DON says, this is not abandonment. Of course, unless you are in a union, she can fire you for not doing what she wanted - in her head - you to do. Or maybe staffing went Dixie and she had to throw somebody under the bus, and you were the lucky one. Maybe she wanted to pull the nurse you reported off to and put her on another unit, and forgot to communicate it. Things get squirrely during weather emergencies.
With that said, I'm going to differ from the crowd here and say it's premature to get a lawyer. You can't "get ahead" of this. BONs are aware that managers threaten to report abandonment all the time to get you to work. But if and when you ever do hear from the BON, IMMEDIATELY get a lawyer. And I agree with other posters here, don't communicate at all with your former employer. There's no point, your DON is never going to change her story, she's either going to try and report you or she isn't. And anything you communicate could be used against you if the BON ever did investigate. For example, your offering to work double suggests you knew there may be staffing issues. See what I mean?
But what I WOULD do is right this minute sit down and write down every single detail about the incident. Who said what when, who you gave report to (including contact information if you can somehow get it), how many patients, who witnessed you giving report, where you were in the building, etc. Keep it somewhere super safe for your lawyer in case the BON does ever contact you.
I especially like the part about how the DON says you abandoned your post because you left without telling her. Sorry, Miss DON, a nurse leaving at an inconvenient time and making YOU feel abandoned is not an issue the BON cares about.