If that is your reason, know that unless you manage to get first blood and snowball very early, then Doran was a complete waste of gold, and since you didn't had Spellthief's Edge, you will find yourself extremely behind when compared to the enemy support, assuming that they started with a gold generation item.
Also, these are the only real perks of Doran's Ring, as Spellthief's Edge is completely superior on every way. It generates gold, it has better mana regen, it is cheaper, and it builds into items that can be useful later in the game, while Doran's Ring doesn't build into anything and you have to sell it eventually.
Laners buy Doran's Ring because they are allowed to farm, and thus, they can compensate for all those downsides. As a support, you can't afford to waste any gold, and Doran's Ring is a waste of gold unless, as I said above, you manage to snowball early. If you really want health, buy a
, since it comes with health regeneration, too.