I've never read anything about the dress itself but think it very unlikely that for the simple style of a young girl's coming-out dress, that a designer as such would have been used - at least in the sense of a top-notch known couturier. The dress would indeed not have been off the peg, but the style could easily have been modelled on gowns produced for her sisters or the huge female cousinage, and it was very common at the time for women with new designer dresses to let their female family and friends (and more importantly, their family/friends' maids) take a look at the latest fashions for their own dressmakers to copy or adopt. However, Germany wasn't deficient in dressmakers who knew the latest styles - in 'Dearest Missy', the correspondence of Marie of Edinburgh and her daughter Marie of Romania, there are frequent references to a 'Mme Menier' in Coburg who seemed au fait with the latest Paris fashions and from whom Marie of Romania was ordering clothes after her marriage (along with Paris gowns!). There were plenty of magazines and illustrations of designer dresses from houses such as Worth which local dressmakers could reference, and if something a bit more sophisticated was wanted, Frankfurt was pretty close to Darmstadt and the dressmakers there could certainly supply a suitable gown. So it could have been a purely local production, with the style having input from the more fashionable family members, or it could have been from one of the larger German fashion centres (though this was unlikely to have been Berlin).