One problem with a crossover between the two universes is that Alice's adventures were clearly identified as dreams, while Dorothy's (contrary to what the MGM movie would have you believe) were not. There are certainly ways to get around that (maybe Alice visited an actual place in a dream-state, or her dreams brought Wonderland to life, or something of the sort), but it's still a key difference between the two series. And Wonderlanders, as Ray Bradbury pointed out in an essay I read once, tend to be considerably meaner than Ozites. Still, I think that there's a certain similarity in the two fantasy lands that means characters from one would fit reasonably well into the other. I could see the Cheshire Cat visiting the Emerald City or the Scarecrow attending the mad tea party without much difficulty. And I'm obviously not the first one to think that, as evidenced by some of the already-existing crossovers. The first major one that I know of was The Oz-Wonderland War, a series of three comics with a somewhat misleading name, as the war wasn't between Oz and Wonderland. It instead featured residents of both fantasy lands, together with the rabbit superhero Captain Carrot and his Zoo Crew of anthropomorphic animals, joining forces to stop a Nome invasion. I honestly think the comics could have been done without Captain Carrot, not because I have anything in particular against the super-powered lagomorph and his friends, but because their presence kind of detracted from the focus on Oz and Wonderland. Oh, well. I guess they felt they needed to work a contemporary comic character into the adventures.
There's a more recent comic called The Oz-Wonderland Chronicles, that also contains a crossover between the two worlds. I haven't yet read any of this series, but I have the first issue on order, and there aren't that many others out at this point. I believe it's a semi-annual publication. Anyway, what I know of it involves a college-age Dorothy and Alice having to go back and save their respective fantasy countries.
I've seen several other Oz books that make brief references to Alice's Wonderland, and I feel like I would be remiss if I didn't mention Lost Girls, Alan Moore's graphic novel series that puts a grown Dorothy and Alice (plus Wendy from Peter Pan) into sexual situations. (I haven't read this either, although I'll admit to being curious about it, because it just sounds so crazy.) One fairly recent Oz book to dedicate a significant section to Carroll's fantasy countries is Visitors from Oz. Not the reprint of material from Baum's Queer Visitors comic series, but the novel by Martin Gardner, editor of the annotated versions of the Alice books and The Hunting of the Snark. I've only read small parts of this book, and from what I've heard, it's not very good. I did read most of the Wonderland section, and it was quite uneventful, mostly just consisting of the characters telling Dorothy and her friends that Carroll had misrepresented them. Not a bad idea, necessarily, but Gardner really didn't do anything with it other than have one character after another complain about Carroll's portrayals.
Personally, I recently came to wonder if the Red King and Queen might be former rulers of the Quadlings. And I remember The Dictionary of Imaginary Places speculating that Omby Amby might be related to the White Knight.