It looks like an aboriginal axe head to me. It is the right shape and appears to have an edge all the way around. There are a couple of spots where the rock has chips broken from it. These have flaked away in shards as would be expected with an aboriginal stone tool. Cement tends to break in random clumps.

I have a couple of aboriginal axe heads made of similar material. As kids we used to visit aboriginal camping sites where the ground was  littered with flakes of flint, chipped away as the aborigines made their tools around the camp fire. As a young farmer we would occasionaly turn up stone tools when cultivating the paddocks. I have a collection of around twenty stone tools now.

It needs to be remembered that Aborigines worked with the stone that was available to them, or that they could trade with neighbouring tribes. This was not always nice flint, but sometimes more of a fine granular type stone. The axes where first chiped into shape by hitting with another rock. If flint type material, they where left as chipped, but for the more granular sedimentry type stone. The rough cut axe head was then rubbed on another rock to shape it. Similar to a woodworker using sandpaper to shape a piece.

I would not be scratching it too much, as this would detract from its collectability and value. The axe heads are rarer than grinding stones and have a bit of value. I have seen them sell at auction for $50-$100. each, but this was many years ago. . There is a greater awareness now of aboriginal heretige than there used to be and there may now be restrictions on the sale of cultural items.