Tom
This indeed looks likes a quote from Rumi, 'God sleeps in the mineral, dreams in the vegetable, stirs in the animal, and awakens in the fusion of the completed Man/Woman' (one version).
I would guess any document attributing it specifically to Kabbalistic literature is incorrect. As you say, an Internet search will reveal that this phrase and many variants has been appropriated by everyone from the Druids to the Theosophists! In terms of Kabbalah, as pointed out by the previous post, Steven Turner, this *could* potentially be seen as a 'four-worlds' doctrine in terms of the Kabbalah. However, all the items listed, mineral, vegetable, animal and man, not only have overlaps (i.e. man is composed mainly of water and salt crystals, which are mineral, has the same qualities as other mammals, etc ...) but only can each be considered in terms of the four worlds, depending on which context you are applying. So, I don't think it is a useful or consistent mapping. Again, as pointed out, there is no 'concordance' of the Kabbalah, as the 'Kabbalah' may be viewed as an oral tradition, whose literature comprises of many works, including the Zohar, Torah, Bahir, etc. and many commentaries written thereafter.
Hope this assists, if you know which 'document' or book made this attribution to Kabbalah I'd be interested, as then I could strike it out of my reading list! LOL.
In the Great Work
Frater F.P.
http://www.templum.com