Leatherworking isn’t actually all that useful for a Paladin (of any flavor).
Your Retribution Paladin will almost certainly be in a group that can use Drums effectively (i.e. a dps group). However, they’ll be in that group with a Rogue, a Feral Druid an Enhancement Shaman and probably a Hunter - all of whom will take Leatherworking as a matter of course. So while it’s potentially useful for your Retribution Paladin to have Drums, chances are it’s unnecessary.
Your Holy Paladin is going to be planted firmly in a group with a pile of healers, so they don’t need Drums at all. At best, it could be argued they might use Drums of Restoration. But Drums of Restoration are so weak that it’s normally better to just have your healers take professions like Enchanting for the individual benefits rather than try to buff their group. Especially when you consider your Holy Paladin themselves won’t particularly need the Drums once the damage starts flying and they start crit’ing.
The leg enchant is just a trade good, so there’s no reason to be a Leatherworker for it.
Alchemy is a traditional profession for a healer. However, you won’t get the really good trinket until SWP and the main reason the trinket is so good for healers is the 40% additional mana from potions… which isn’t all that great for a healer with Spiritual Attunement, Illumination and limited ways to spend massive amounts of mana in a short period of time.
Jewelcrafting is a bit of an odd duck. It provides trinkets that are decent enough for any given role, but rarely BiS for any role. It provides some unique gems that are minor upgrades initially and purchasable by anyone in SWP. It provides BiS necks very late in the expansion. So it could be considered good for any class/spec, but not exceptional for any.
Gathering professions are normally not taken (or, at least, kept) by raiding toons since they provide no raid benefits. If you need materials, just farm other stuff and use the proceeds to buy them on the AH.
If you plan to swing a weapon at all, you’ll normally want to pick up Blacksmithing or PvP - at least initially. While you’ll get better weapons long-term, your weapon is the most important item you carry so being able to accelerate gear acquisition there is incredibly helpful. Blacksmithing also provides some BoP raid drops for Paladins.
Engineering can be useful, especially if you have multiple roles in mind for the same character. However, the helms don’t appear until Black Temple (which would likely be a ‘phase 2’ or later if they release that way).
Enchanting is generally consider the best overall profession since the ring enchants can be helpful for anyone and they’re just a flat addition to whatever else you’re doing while the value of the other professions varies quite a bit based on what gear you’re seeing from raids.
Lastly, Holy Paladins are arguably better at AE farming than Protection Paladins. The top half of the Protection tree is primarily useful for holding threat or dealing with raid bosses rather than increasing AE output or surviving a large swarm of minor minions.