Between some of the comments on this question and a conversation with my brother, I think I have found an answer. Unity figured out the way to save Rose's life through logic, and not through access to information that the Dream King doesn't have.
Dream is reluctant to try to research and understand vortices because they are so dangerous -- he once lost a world to a vortex ("Lost Hearts" page 5). He would much rather just destroy them, and not dwell on their nature too much.
Unity, however, does care that her granddaughter lives. She understands that there can be no bargaining with Dream on this, because he will not suffer the loss of another world; therefore, Unity offers herself in place of her daughter. Although Dream doesn't understand it, Unity has a sound logical proposal for taking her descendant's place:
Unity: I want you to reach inside yourself, and give me whatever
it is that makes you the vortex. Give me your heart.
Unity: Rose--I'm dying. We don't have much time. You're dreaming.
Anything's possible. Just do it.
(page 13 -- emphasis in the original)
Unity also makes reference (page 13, quoted in the question) to Dream's being "not very bright" -- his issue is not missing information, as I originally thought, but an inability to reason out another solution to his dilemma.
Another support for the theory that Unity's solution was based more on logic than on privileged information is in an earlier panel (bottom of page 8), where it is revealed through narration that Unity "finally understands" the Dreaming.
Or, as Radhil put it (albeit with fewer sources):
Dream doesn't appear to have peered too closely into the full natures
of the vortex, given that his hesitance to just end them created
disaster in the past. As for why Unity knows what to do... dream-logic