If the animals don’t go grey, then you can; or if you hit up the animals in hellfire. Eg I know rich thorium greys out, so the same idea can’t be applied to old world ore veins, but if you manage to do a lot of fel ore veins before hitting 60, then you can get 375 mining. (in my case, I reached 375 mining at lvl 61, that was with rested exp from lvl 59 already. I quested into 60 but after that just killed mobs as I went mining)
Keep in mind if you’re doing a lot of skinning more than levelling, then you may hit 375 before you hit 60.