We don't "drop" the /n/, but it does undergo a change - English nasal consonants assimilate to the place of articulation of the following consonant. Thus rainbow is pretty much always pronounced rai[mb]ow, raincoat is rai[ŋk]oat, etc.
As for how this explains your daughter's spelling, consonant clusters are "difficult" in language acquisition, and young children very commonly simplify them. In addition, syllable codas are less psychologically prominent than syllable onsets (and some very young children just delete them across the board). Here, my guess is that the nasal assimilation process makes it particularly hard to perceive the nasal as a distinct phoneme from the subsequent consonant, so your daughter leaves it out from the spelling.
By the way, there's another major allophonic change with nasals in English that is worth mentioning: they nasalize the preceding vowel. So we pronounce lunch as [lʌ̃ntʃ]. This is hard to perceive, but if you record yourself saying (for example) met [mɛt] and men [mɛ̃n], then clip off the final consonants from the recordings, you'll hear a distinct difference in what is left.
Though I've never read anything about this, I'd speculate that in fast speech - because the vowel is so much longer and more salient than the nasal consonant - most of what alerts us to the presence of the /n/ (perceptually speaking) in a word like lunch is the nasalization of the vowel.