I have a few thoughts, and lots of experience: my DS1 was excluded more times than I can count, for 0.5-10 days. :( The following assumes your DD is at state school in the UK...
If your DD is currently excluded for a single day, it is very unlikely that the next step is permanent exclusion: one day is a relatively minor exclusion, and the head had the option of a longer exclusion or immediate expulsion, if the offence was serious enough. It sounds more like she's going for shock tactics, I'm afraid.
If she wishes to permanently exclude your DD, she will have to involve the governors: she cannot make the decision by herself. Most governors will back a head teacher, but it does give some protection from clearly excessive or unfair punishments.
You have a right of appeal.
The local authority will also be involved. Your DD must be educated, and the LA will have to find her another school place if this head throws her out. For this reason, LAs do not encourage exclusions, though they no longer have the power to stop them. You could consider phoning them for advice; I found mine helpful and reassuring, on occasions when the school was being unhelpful.
There is also an org called ACE (advisory centre for education??) that provides good information and advice. They have a website and part-time phone line for parents: www.ace-ed.org.uk
One of the things I found most stressful and upsetting was that some school management team members treated me like an 'enemy' when my DS was in trouble, not realising that I was struggling with him too and could have done with their support rather than bullying. I learned with senior team members were fair, decent human beings, and tried to deal with them whenever possible. You may be able to find a deputy to deal with instead of the head...
If push comes to shove and your dd does get expelled, this may not be the disaster you fear. I fought to keep my son in school, but with hindsight he may well have done better at a different school with a more relaxed approach and a head teacher who didn't dislike him so much. Another boy I know who was expelled went on to thrive in a different school, his self-confidence was less damaged than my son's, and he did not become alienated in the same way.
Good luck.