What is the reason for piercing her ears? Do you come from a culture or a religion where this is required or emphasized? If so, you can ignore what else I'm adding here, and follow your religious beliefs or cultural norms.
Otherwise, I think you see the risks of piercing a toddler's ears. Kids move/squirm, the earlobes are so small that an average-to-good technician can't always guarantee even placement, and of course they fuss with their ears and cause irritation and even infection.
I agree with you not to re-pierce the ear and have 2 holes so close together.
Barring a strong cultural imperative, I'd take the earrings out, let things heal, and wait until your child is 10 or so and really wants earrings and is able to maintain them. I know that there was a time when people pierced little girls' ears if they had little hair or otherwise "looked like a boy." But that changed decades ago when men started having pierced ears and people gave up the idea of girls-pink/boys-blue and the need for the public to be able to label kids by gender. Other than ear piercing and infant/toddler headbands with bows, I think most people have moved beyond that.
Maybe she won't even want earrings. Maybe she'll want to choose her own. Maybe you will wish you didn't have to spend money on more earrings. There are so many years ahead of you to enjoy your child growing up, it's just a shame to rush things and then have these sorts of problems. There's truly no hurry, and you're precluding the fun of doing this when she's old enough to make her own choice and take you with her.