In bridge, what are the proper followups to a Jacoby transfer?
Well, the proper followup is what you have agreed upon.

The 'normal' responses to a transfer allow you to bid the major at the 2 level (usual completion of the transfer) or bid the major at the 3 level, which shows a maximum hand and 4 cards in the major in question (called super-accept).

Assuming your agreement is the above, bidding 2NT with doubleton in the major, instead of completing the transfer is just silly.


You partner could have 6 cards in the major and a bust hand and might have been planning to pass the 2H bid from you. With a 6-2 fit, 2H will play very well as compared to 1NT. Even with a decent 5 card suit and nothing else, 2H will likely play better than 1NT. 2NT might just be too high. This is because the trumps serve as stoppers in other suits, and also provide entries into dummy.
With partner having an invitational/game forcing hand and exactly 5 card major, you will always be able to reach 2NT or 3NT when you need to. With an invitational hand and exactly 5 cards in the major, partner will rebid 2NT, which you can then pass (or go on to 3NT if you have a maximum hand). With a game forcing hand and 5 hearts, partner will bid 3N. 
You are denying partner the chance to bid 2S after transferring to hearts which can show some hand types (some people play it as 5-5 in majors etc).
Bidding 2NT is a unilateral bid. Remember that your partner is the captain. You have narrowed down your hand with your 1NT bid.


So violating the transfer to bid 2NT to show doubleton is pointless with no real gain (you will always get to deny support later), and has only downsides.

Also, from a system point of view, having 2NT show a doubleton is inefficient, as later followups will clarify that situation. You are just wasting space and getting to a bad contract/wrong siding it for no reason.

That said, some people do have followups other than 2 or 3 of the major, but those typically show 4 card support and some other feature (like doubleton/values in the suit bid).