Alice's Adventures in Underland: The Queen of Stilled Hearts, I'm happy to say that no such problem exists. The book is utterly charming (provided, of course, that you're the sort of person who enjoys phantasmagorical settings, humorous and/or macabre nonsense, and zombies).
I was expecting something on the order of Pride and Prejudice and Zombies -- that is, the original text of Alice in Wonderland but with zombies added in. That would have been enjoyable by itself, I think, and there are definitely zombies in there. (In this case, it isn't so much that there are zombies "added in" as it is that all the mad inhabitants of Wonderland are now zombies. Still mad, though.) However, the author doesn't stop there. Alice's Adventures in Underland isn't just Alice in Wonderland retold, with zombies; it's also a story about Alice Liddell, the young girl for/about whom the story was written, and something of her experience growing up in an alternate-history England where the zombie plague is wide-spread, but held in check by a special serum that allows the infected to look, act, and think like everyone else.
On that level, it's a fascinating look at the society of this not-quite-historical England, using the not-quite-Alice-in-Wonderland story as a sort of lens or mirror to explore elements of social expectation, hypocrisy, slavery... and, of course, zombies. And, by providing this not-quite-historical context, the author makes the story much more accessible than (I suspect) most casual modern readers find the original Alice in Wonderland. Alice in Underland isn't just charming, sometimes macabre nonsense; it's charming and sometimes macabre nonsense with meaning.
If that sounds like your cup of tea, you can purchase the book here. Just don't forget to take your serum.