A bit rough because it was made from offcuts found in the scrap bin. However, it works very well with a small dog.
The base layer is 180mm by 130mm. It should be thick enough to hold a treat when drilled. A forstner bit works best here. The pegs are 30×30 and 38mm deep. It would be much easier to use dowels for the pegs, you could then simply drill holes in the second layer instead of building up a lattice. For big dogs, just use a baking tray and tennis balls.
My own invention, treat this one as experimental and definitely needing improvements. There are three layers, 210mm diameter. The lowest layer can be quite thin. The middle layer needs to be thick enough to hold the treats, say 12mm. A top layer of 8mm is satisfactory. Drill all holes then glue the centre dowel and the lower two levels together, or make the dowel a very tight fit and mallet it in.
I glued and screwed the lump for turning. It got chewed. It might be better to use several smaller lumps. The top layer needs to turn freely. To stop it coming off, drill a horizontal hole through the dowel and fit a washer and split pin.
A possible improvement would be to glue a non-slip surface to the bottom.
This alteration worked. The dog pushed the top disc round with its nose. The pegs are just glued on.