DD is a very good local school leafycomp in mn vocab.
One of her teachers really helped her and any many of the other students. She answered emails in the middle of the Easter holidays, took them on special trips for the subject during the weekends and generally went the extra mile. All her subject class got outstanding results including DD and I wanted to thank her personally. Without her help there's no question that DD would have got her Uni place.
Would you suggest a letter from DD, a letter from me, a letter to the head or a bottle of something cold & fizzy?
Definitely letters to her not to the Head - it's so much more personal and the Head might not pass things on.
If it were me, I would prefer a letter from DD and a bottle of fizz - if you wanted to go for a present. Or just the letter. I still have letters that students wrote to me 15 years ago.
One of my A Level students got me a DVD of the concert version of Les Mis last year - she knew it was one of my faves, AND we'd done it as the school show that year so it felt really personal. Gifts are not necessary, of course, but that's not to say that they're not very much appreciated!
Letter / card from DD (and one from you, if you really want). That would mean the most to me, as an A Level teacher.
Does DD have a photo of her with friends from the same subject group? Maybe get that printed off. Otherwise wine sounds like a great gift!
I would also email the head to praise this teacher, mentioning all of the things she has done for your daughter and her peers. There's no reason why the head would know how hard the teacher is working if the school is anything like mine unless the teacher is particularly effective at blowing her own trumpet (she doesn't sound the type) and even then a parent endorsement means a lot.