You mentioned "precision rifle that I can hunt with".
You could potentially hunt with any rifle you wish to carry around the bush. As a Precision or Target rifle is generally a heavier stock with a Heavy Palma or Heavy Varmint contour I doubt you would want to be carrying one of these around in the bush for very long. If you are hunting from a stationary position then it would definitely be feasible to get away with a heavier rig.
As most people like to have the lightest gun possible when having to pack it on their shoulders, if this is your case, then I would buy/build a gun specific to those needs.
I am sure there are many rifles out there that are used for both hunting and target, I doubt that the target portion of the shooting would be as competitive as a gun built for that purpose specifically.
There are guns built for "Sporter Class" Benchrest competitions where the rifle must weigh under, I believe, 10lbs (usually a mere fraction of an ounce under this target weight). If you would be comfortable carrying around a 9lb 15.5oz gun around the woods then this may be something to look into.
Don't get me wrong, I would be the first to encourage someone to come out and "run what they brung" in a match just for the shear fun and learning that it offers.
There have many threads on this and the consensus has been: Build a Hunting rig for hunting and build a target rig for competition.
Think of motorcycles: Crotch Rockets are built for road use and Dirt Bikes are built for Off Road, the crotch rocket would be the s**tz on the dirt and the dirt bike would be the s**tz on the road. You could buy a Dual sport that would be sufficient for both, but would never do as well on the road as the rocket and the same holds true against the dirt bike off-road.