How to complete [Fun for the Little Ones] with low Archaeology skill?

I'm trying to complete the quest Fun for the Little Ones in order to get the Faire Favors achievement at the Darkmoon Faire. However, I had never levelled my Archaeology up until now, except for (apparently) a few points some years ago.

So first I levelled my archeology to 75 in Shadowmoon Valley, which was required to get the quest at all. Now that I got the quest however, it turns out I need 15 "Fossil Archaeology Fragments". It seems I already have 11, but I don't know how to gather the remaining 4.

I've tried several things:

• Go to Brann Bronzebeard in Pandaria to trade "Restored Artifact" for some fossil fragements. This requires a skill level of 600 though.
• Similar story for the Arakoa sales guy in Stormshield, Ashran.
• Read through Wowhead's Archeaology Guide.
• Check for any tooltips or explanation in game for the Archeaology profession window (which tells me little to nothing).
• Click around the World Map, check some of the starting zones in old Azeroth to see if there's dig sites there where I could go. (Perhaps I've overlooked it? Should there be some zone with dig sites? I do see dig sites in Shadownmoon Valley, Draenor, but no fossils pop up there.)
• Read a lot of comments on various Wowhead items (e.g. Black Trilobite fossil, as well as other sites like Wowpedia and WowDB. No dice.

For what it's worth, here's what my profession looks like in game, currently:

Help me out here, how does this work? Or am I stuck, do I need to level to 600 to be able to finish this?