If you have an actual boat already, either the karve (this moves pretty easily) or the longship, you can also sort of push yourself underneath the water a bit with that. The jump gets you to drop farther down, but i found wedging myself under my longship to be a decently effective way to place underwater supports for a dock to...though actually seeing what i was doing was an entirely different related issues.

Later on you may discover a way to drag things out of the water before murdering them (or drag them around in general) but that's really the only options you get for recovering underwater loot besides that some of it (like wood for example) floats. Otherwise its mods or console commands (console doesnt let you dive, but you can turn off the swim effect to run along the bottom for things like loot collection or building). Luckily, deer are plentiful so in this case it's not the biggest loss. Just have to wait a bit longer to find some more. Lesson learned for a relatively low cost, not a bad outcome in this game.