I gotta tell ya, this is a tough one, but you'll be glad you did it (when it's over, not during). When it comes to dining, newborn babies think they're on a cruise ship, and at midnight and 2 a.m. they fully expect (and demand) a buffet.
When our little guy started crying for food at two in the morning, my wife had to get up because she was breastfeeding, but I got up right along with her. I sat there and kept her company, we shared stories about our day, marveled at how cute our baby was, etc., until it was time to burp the little guy, then she'd pass him over to me and I'd burp him. I have to say, I really enjoyed the burping because even though my wife could surely have burped him herself, this way I was at least helping in the process and that felt good. Plus, I was getting to hold my little buddy and the burping helped him too.
It sounds corny, but these late-night feedings were really a time of great closeness for my wife and me as we sat there in the dim light, fighting to stay awake through the feeding, and we both look back on it with great fondness, even though it was incredibly tiring. I remember one night -- it was like four in the morning -- and we were up trying to change our son's diaper, and he was just screaming at the top of his mini-lungs and kicking his little hands and feet. He was beet red and just as pissed as he could be. I held this screaming little baby out away from my body so my eardrums didn't explode, and I looked over at my wife, and we were both so exhausted that we simultaneously burst into hysterical laughter. He didn't find it funny, but he paused long enough for us to change his diaper. We kept giggling for 20 minutes until we put him down in his crib, and then we literally fell into bed.
Was it hard getting up numerous times a night? Yup. Would I have wanted to do it alone, all by myself? Nope. I don't imagine my wife would want to either, and that's why I was there. Be a great dad, and be there with her for all the feedings. I promise you, it'll kick your butt some nights, but you'll survive, and you'll look back with fond memories. Hey, I said having a kid was wonderful. I didn't say it was easy.