my best guess is that it's transliterated from jutland in british english, according to cantonese. here's the rationale:
the earliest book mentioned jutland in chinese, is "海國圖志" by 魏源, which was published in 1843. in its preface, mr 魏 stated that his book is derived from 林則徐's translation of a foreign book "四洲志".
in "海國圖志" volume 58, page 44-66, the entry of "嗹國" (the old name of denmark in chinese) stated:
lolland --> 臘蘭, funen --> 府領, zealand --> 西蘭
imo, cantonese perfectly transliterated the british english, in the translation of 府領 & 西蘭.
copenhagen --> 戈西哈林, 哥卑納給
københavn --> 可品哈
again, 可品哈 in cantonese is, perfect match of danish "københavn"
jutland, initially is transliterated as "人德蘭"
i suspected "入" is a typo error of "人" here.
in another book "瀛寰志略" by 徐繼畬, printed in 1848; the entry "denmark" is in volume 4, p73-79, jutland was also translated as "人德蘭".
back to the question
When was Jutland first written as 日德兰? What dialect was being used to make this transliteration?*
i think cantonese was used. compare "府領" to funnel, "西蘭" to zealand.
about the time, it must be later than 1848.
prior to these two books, info of europe countries were rare, and brief. so, jutland in chinese, was first introduced in 1843, by mr 林.
so, why 人德蘭 changed to 日德蘭?
well, using the character "人" in places name is, very awkward . e.g. "people of jutland", it would become "人德蘭人". most likely, someone thought the same, then changed it from 人 (yan4, low level tone) to 日 (yat6, low entering tone) such change preserved the low tone and the phoneme /a/.
just to remind, such is my guess only.