It is a great idea, but it makes more sense when the recipient does the registering IMO.
If you are unlucky enough to have to get medicine into a baby, something has happened and you are hopefully under the supervision of a doctor or a nurse who can aid with the practicalities.
Small babies are delicate machines and gifting any sort of medical aid "just in case" might give the recipient ideas. Feeding a baby cough syrup may have been just an example but sounds downright dangerous. Please be careful.
I realize this was just a casual example, but kids under two generally shouldn't be given any cough or cold meds (there are no over-the-counter cough meds for kids <2 sold in the US).
Definitely still useful for other meds though.
I didn't m to sound facetious but now I'm thinking about the ways of making a SaaS out of this : the incentive for the giver is easy enough ; the card maker gets a cut ; AWS should give you a great deal on hosting..
So she bought an Amazon gift card. And then she created a wishlist of items she thought the mother might need, doing the research to find reputable brands, unique solutions to problems, "best mom gadgets", etc (such as the pacifier that you can put liquids into; it lets you get liquid medicines into the baby, like cough syrup, without stress). She sent the gift card, and the link to the wishlist with an explanation.
It was both a pragmatic and thoughtful approach, without the risk of buying something she already had, or didn't need or want.