DH teaches at a German university and I used to (and until recently was on the selection panel for a degree course here). What the PPs have said is true - while the actual fees are very low (perhaps a few hundred euros per semester), there is very little pastoral support and some classes, especially in the more traditional unis, can be enormous - particularly for subjects like business and law, up to 300 or 400 students, people sitting on the floor, etc. Most students are older and more independent than is average for school-leavers in the UK, so there is less of a university 'system' laid out for them. Many students have to work to support themselves through uni (loans/grants are only for low-income families). There's less of a campus model, so many Wohnheime are a long way from the actual university and quite socially isolated. German professors are notoriously arrogant and inflexible (well, some of them), the system is far more hierarchical than the UK, and undergrads are the lowest of the low. So your DD would have to be pretty confident and a self-starter. On the other hand, I moved to Germany when I was only a little older - 21- and just turned up by myself with a rucksack, no German skills, and made a go of things from there. It's doable.
And it's right that a German degree would be aimed at German native speakers, so it wouldn't inherently improve your German skills more than simply being in the country and picking it up from all around you - in other words, it's purely literature, not a language-learning course. However, many universities do offer a one semester or one year 'preparation' course which teaches German language skills to prospective students - but that doesn't count as part of your degree. You need to ask about DaF (Deutsch als Fremdsprache provision).
Have I put your DD off yet? 