I obviously haven't seen the model in its damaged state, but I may be able to offer some suggestions - based on a fair amount of experience in restoring old ship models.
Do you have all the pieces of the broken bowsprit? If so, it's advisable to fix it rather than replace it, if possible. And it probably (not necessarily)
is possible. Remember that modern adhesives are considerably stronger than wood.
A good, inconspicuous trick is to drill a pair of holes in the adjoining ends of the broken pieces, insert a piece of wire (cut to the appropriate length) into the holes, and glue the pieces back together. Franklin Titebond or Elmer's Carpenter's Glue are excellent adhesives for such purposes. If a few splinters are missing, or for some other reason the joint isn't quite smooth, a little wood filler and sanding should make things right. (My favorite wood filler is Famowood brand.) If all the fragments have survived and you line them up carefully, this technique will produce a bowsprit that's stronger than it ever was before.
If the Labradors absconded with part of the bowsprit, you have two options: splice a new piece onto the remains of the old one, or extract the remains from the model and make a new bowsprit. In either case, it's desirable to use the same kind of wood that was used for the original. I can't tell from the photos, but if the model is fairly recent (built within, say, the last fifty years or so) there's a good chance that the spars were made from birch dowels. The dowels stocked nowadays by hobby shops and lumber yards generally are made of either birch, oak, or some East Asian species that I can't identify. Try to match the original.
I can't tell from the photos just how the bowsprit is shaped. If it's round throughout its length, and tapered, you probably can reproduce it pretty easily by chucking a piece of dowel into an electric drill and holding a piece of sandpaper against it. That technique takes a little while to learn (buy some extra dowel for practice), but my guess is that in an hour or two you'll be able to turn out a nice-looking bowsprit.
The trickiest part of the project may be matching the color of the original. (That's one reason why it's preferable to keep the original if at all possible.) I gather the original is finished with wood stain. A good way to deal with that problem is to buy some of the felt-tipped "touch up stain pens," which are made by Olympic and Minwax. (They're sold in paint stores, and places like Lowe's and Home Depot.) These pens contain genuine, solvent-based wood stain, and come in quite a few colors. You can mix colors to get a close match for your original. Finish it with a couple of coats of varnish or shellac (whichever matches the original most closely), replace the damaged rigging (easier said than done, but the rigging of a J-boat isn't very complicated), and you're done.
That's about all I can offer without seeing the damage close up. Hope this helps a little. Good luck.