Don't worry about hiccups!
Hiccups are caused by a muscle twitch in the diaphragm. The twitch can be triggered by eating/drinking to fast, swallowing air, laughing/crying, and a bunch of other things. It's not dangerous and usually goes away on it's own. Babies get hiccups all the time because they're muscles (including the diaphragm) are still developing. Plus they're learning how to suck and swallow, which can lead to swallowing air, which triggers hiccups.
Don't worry and get out the video camera. Baby hiccups are adorable!