The biggest difference will be your hit rating. At 68, you lose a lot of DPS on the bosses and some trash in UK from lots of misses which makes all the fights a lot longer than they should be. Once you get to the 72, you should be hitting a lot more which and have small stat increases that you'll notice.

Without a question, it'll become a lot easier, I remember trying UK on my shammys @ 70, and got smoked hard. At 72, it was a little easier, but still not doable. At 73, I could clear most of it, but still had to get another level before I finally cleared it. Part of that had to do with group makeup as well.

As far as your group make up goes, heroics will start off hard, but as you get a little bit of gear, you'll quickly outgear them. I was running 5 druids (bear,3xboomkin,tree) through heroics in pretty low gear (iLvl 187 and lower gear), and was managing just fine. Since you have 3 shammys in your group, @ 80 you'll be able to set 3 focus targets as well, and Hex them through each trash pull making it a lot easier.