The secondary profession dailies only award 125 (base) reputation each, you're not missing out on much.
A single egg gives about the same rep, although I've personally only ever saw one. I wasn't exactly looking for them and I'd rather do a few extra days of dailies than flying around cliff tops. That's what I did for my main character, I got the rep purely from dailies and the quest chain and it didn't take long at all. Most alts have got it at exalted from all the Timeless Isle eggs I found.
I've been able to get from Neutral to Exalted in one day by doing the quests (excluding the profession quests) and gathering eggs. Granted, this was before realms started merging, and I already had one character at Exalted at that point.
It shouldn't take long. Just do the dailies every day and throw in a few egg runs every now and then.
"We don't care what people say, we know the truth. Enough is enough with this horse s***. I am not a freak, I was born with my free gun. Don't tell me I'm less than my freedom."