First let's clear up the "touch" vs. "hug" business.
As has been discussed many times before, some say the prohibition is "any touch whatsoever"; others "only affectionate touch." In some circles I'm shomer negiah means "I follow the stricter opinion and won't even do non-affectionate touch (as opposed to those who do business handshakes)"; in other circles I'm shomer negiah means "I don't do affectionate touch (as opposed to my HS/college classmates who keep shabbat and kashrut but hug and kiss their boyfriend/girlfriend").
A previous revision of your question included the phrase:
touch her in any way whatsoever: I think even a friendly touch on the shoulder in greeting will be forbidden.
I'm reminded of the Snake's discussion with Eve: Touch the tree, eat the fruit, whatever all the same. "A friendly touch on the shoulder" could very well be considered "affectionate." An example of "any touch whatsoever" would be a business handshake, or taking someone's pulse.
Okay, let's try this again. The prohibition on "negiah" is "affectionate touching", and according to some opinions, "any touching." At what age would that begin, according to either opinion?
(Rabbi Neustadt is quoting a novel piece from a student of Rabbi Shlomo Zalman Auerbach about age 3; I don't think that's common practice. Rabbi Mordechai Willig cites it for theory's sake in an mp3 on tzniut, exclaiming his surprise.)
Well, the prohibition is based on avoiding people who are erva (prohibited relations). Your cousin is not a prohibited relation per se, however once she (or any other unrelated woman) reaches menarche that changes. So around 11 seems quite reasonable.
Rabbi Moshe Feinstein elsewhere wrote that with regards to extended families that do lots of hugs, we view it as gross, but not risque, for a grown brother and sister to hug and kiss. We still prohibit it, but there's some more room for leniency in cases of non-observant family who will be offended, or how much the rabbi should protest such behavior.
As Rabbi Joseph Dov Soloveitchik famously said, halacha is a floor not a ceiling; all halacha aside, there will be dictates of good judgment and taste regarding what forms of touch are appropriate, in what contexts, with what age of cousin under the age of 11. It appears that Torah.org says "find a good publication that goes into all sorts of detail on that"; it doesn't surprise me that various contemporary rabbis have tried to record guidelines for every situation, but at some point we hope the answer is simply "use good judgment."