Totally normal. The cause comes from the difficulty of evenly drying a piece of timber that size. The outside dries quickly, but the interior can take years to dry. Drying causes the wood to move and when the outside and inside moves differently, cracks appear.

You can fill the cracks with wood filler, but matching the color will be difficult.

I have the original stain that was used on the timber. Is there a putty I could use that would take the stain the same way as the doug fir?

I doubt it. Most manufacturers advertise their filler will stain---but they seldom match---and some don't stain well.

But, experimenting can be interesting, if not actually fun.

You can get the colored putty used to fill hardwood floors.
The colors can be intermixed to get a closer shade.