I did my first beer using honey last night and the beer is not bubbling this morning as it usually does. Is this normal? Should I re-pitch the yeast or not?
1 smack pack in a barleywine, you say? I've found that bigger beers tend to have longer lag times before the yeast get going, and unless you made a sizable starter, the yeast are going to have to work even harder. If you didn't make a starter, it wouldn't hurt to pitch more yeast.
It will probably also help to aerate/oxygenate again. You're generally safe giving high-gravity beers more oxygen every 8-12 hours or so until it gets to bubbling, but you need to stop as soon as it is, so that there's not any left over after the yeast have done their thing.
According to your recipe you're at 1.052 estimated OG. According to the Mr. Malty calculator that @baka posted, you'd want 2 smack-packs to get to the recommended amount of yeast.
So yes, you probably under-pitched, and that's why you're seeing a lag in yeast activity. However, you don't need to panic. It can take 24-72 hours to see signs of fermentation. I've had side-by-side batches where I pitched the same yeast into both, where one took off within hours and the other took 2 days to get started. They both ended up fine.
Serious under-pitching can lead to stressed yeast and off flavors, but at only 1.052, I don't think you've got much risk of that. If I were you I'd just relax, wait, and let the yeast do their thing.