Thanks for answering my questions.
As I'm sure you know, the Buckeye (Aesculus spp.) is a member of the Hippocastanaceae family, and contains a toxic component to dogs known as aesculin. When ingested, buckeye can potentially produce significant GI irritation, dilated pupils and severe central nervous system depression, possibly leading to coma. In some cases, however, the opposite-central nervous system excitement-is seen.
Of course, that's with a larger amount consumed than your little dog ingested. If it had been less time since she ate it, I'd suggest giving her the peroxide in an attempt to get her to vomit, but since it's been almost an hour, it's a bit too late for that.
I think she'll probably be just fine. Just keep an eye out for any unusual symptoms and if you see anything that triggers a concern, then have her seen by a vet as soon as possible...however, I doubt you're going to see anything. Try to discourage her from eating any more though...she got lucky this time, but eating them regularly can cause the toxin to build up in her system and could cause a problem.
I hope this helps!!