What brand and model of rifle? Folks might can help you find a full sized stock. You might want to hang on to that short stock as you might need it for a grandson before you know it!
If you decide to reattach the cut-off, you do have more options with the laminated stock than a standard wood stock. With a wood stock, you'd not get real good performance with screws into end grain, but with the laminate, screws would hold much better.
Try just "tacking the stock on temporarily perfectly lined up, with a couple drops of glue. Then drill through the tacked on cut-off into the shortened stock, using a bit sized for the screws to "bite." Pop off the tacked on cut-off and then drill out the holes through the cut-off to completely clear the threads on your screws, letting the smaller holes guide the drill bit for the clearance holes. Counter-sink the holes for the screw heads. Spread epoxy on the two parts and "wang 'er down", allowing the squeeze-out to just sit. When it's hardened, file it down flush and refinish as desired.
HINT: If you're going to have a recoil pad, make sure the holes you drill to reattach the cut-off are out of the way of the screws for the pad.
Hope this helps. Dowels or biscuits will still work but I think this'll be easier and more secure.
Rex