If you want to start boosting immediately, go to outlands with your DK and get some tank gear upgrades from the starting quests. They will greatly improve your survivability. I managed to boost a team to 60 using a lvl 62 DK - he dinged 64 by the time the boosting was finished. It went faste enough, but not it was not optimal.

In retrospect, I would have done what the others sugested and get your DK to 70 first. It will speed things up for you in the long run. However, to answer your original question, yes you could boost for a while with a 60. It just won't be as fast and towards the end it will get more difficult.