早稲[Wase] is 熟字訓[jukujikun]. It literally refers to early-maturing type of rice plant. (Incidentally, medium-maturing type is 中稲[nakate], and late-maturing type is 晩稲[okute].) 田[Ta] changes to "da" because of 連濁 [rendaku] there.
As Mike-san pointed out, わせ phonetically has nothing to do with 早稲 as in the explanation in the wiki page I linked above. Or, are you asking about the etymology of the word apart from your initial question, just like where いね, which also phonetically has nothing to do with the Chinese character 稲, came from?
I understood that the sound ワセ doesn't come from the characters 早稲, just like タバコ doesn't come from 煙草. Assuming it's a fusional pronunciation of a native Japanese word (akin to 今朝), I was wondering which words and why they fused as ワセ。
The kanji 早稲 applies only to rice plant(of course). As for other plants/fruits, 早生 is used instead (the pronunciation is the same わせ). 広辞苑 says that the old form of わせ was わさ, but it doesn't mention about the etymology of わさ.