R' Shimshon Pinkus published a sefer called ברכות בחשבון (that's breichos, not brachos) which goes through the song Mi Yodeya and explains the philosophical significance of each one and how it fits in to the chain of the song. His thesis is that the words of the refrain are not מה אחד מי יודע - "who knows what there is one of" - but rather "אחד מי יודע" - "who knows one," i.e. who knows what "one" is. He explains how each chosen item demonstrates and epitomizes what that number represents in Jewish thought.
The ideas are rather complex and difficult to summarize, but I'll do my best:
Nine: Eight represents "למעלה מן הטבע," going above nature, that Hashem is not subject to and can override the natural order. Nine represents something above that - that Hashem is beyond all definition, אין סוף (limitless), and we can only describe Him by what He is not. This, however, is still not the highest level. This is still something we can understand - we understand that Hashem's existence is beyond our understanding. But even that is, at the end of the day, a shade of "definition," albeit a safer one. This is the "presentation" to us, on our level, of Hashem being beyond definition. But above that is the level of לך דומיה תפילה (Tehillim 65:2), to You silence is praise - meaning that there isn't even anything we can express. "Nine" is the level of the realization that Hashem is אין סוף.
This is encapsulated in the process of birth, through which the soul, which is destined for eternal life, and through it man has in him צלם אלקים and an aspect of infinitude, is put into man. This parallels the "revelation" of Hashem's infiniteness being presented on our level - the חלק אלוק ממעל being put into man - the "אין סוף הנגלה והנתפס," the "infinite which is revealed and expressed" (quotation is from R' Pinkus).
Eleven: I am going to majorly oversimplify because he goes on for pages developing this idea. Eleven is the number which represents the sitra achra, the "negative side" of spirituality, as well as the ability to overcome the sitra achra. R' Pinkus goes at length to explain how and why this is so, but I won't attempt to do it justice here. The eleven stars in the dream represented the ability of the brothers (as part of the greater picture of the thirteen stars, as there were actually thirteen stars in the dream) to vanquish the sitra achra.
I suggest reading it (and the rest of the book!) inside to actually get what he is saying.