the administrator in question replied that I am illegally using the employer name, and she will forward the case to the disciplinary committee
She is being very silly and her "threat" is fairly immature, but she has pointed out that you have made a mistake. Easy to fix, remove it from your footer, will not lead to legal issues so don't worry about it!
The longer version:
This question has fairly legal connotations and therefore depends on the jurisdiction you are in. I can only speak for the UK but you would need to prove the act occurred (which they can from the email - the "actus reus") and the actual intent to commit the act (the mental intent to commit the act or "mens rea" - which they would have a pretty hard time proving here).
Even after actus reus and mens rea, in the UK you cannot just take someone to court and expect a large lump of cash to come from it, you also need to prove loss or damage, otherwise you are going to "win" technically but actually lose because you just went through a court case and got nothing in return for your "win" except a hefty legal bill (which the court can actually decide you have to pay if you lose but that is assuming this would get to court, which it wouldn't - EVER).
All of the above is totally moot though since this person is suggesting sending this to some disciplinary committee that surely has no bearing on your current employment and even if they did, should have the competence to see that this was an honest oversight on your part, not some criminal mastermind trying to use an email footer for nefarious means.
I would however take the time to respond (after ensuring you have removed the footer message) and let her for know you've fixed your mistake and that you have removed the email footer from future email.