Welcome speedfreak,
The conversion is no problem, as Netz said, just a straight barrel swap. 308 is a good round too. To answer the question about how far is your is the 22-250 good for, has alot to do with how far is the shooter good for...
pdogs at 300 is no problem, Do-able as far as 500 if the wind is not bad. The drop for the 250 and a 40gr pill and 200 yd zero will be in the 40"+ range at 500yd. but the 308 with a 168 gr bullet will fall 50"+. The wind will effect the 250 much more then the 308. I had a model 12 set up as a 308 for a year or so. The barrel now lives in a tube and a 6 br is in its place for the longer ranges. Im much happier with it, still have a 22-250 for thump'in critters too thou.