I seriously considered changing the spelling back of my son's name, to the original way because it's a bit unusual, but changed my mind at the last minute.
You have a year post-registration of birth to change it. On the long birth certificate that's re-printed, the bottom section 17 will say name after registration - the new spelling basically. It wouldn't eradicate the original spelling, in fact that version would be the first name on the form at the top still.
My son's name people misspell allllllll the time, so i don't think formally changing it would have stopped that, people do all different ways naturally anyway.
In common usage, you can teach your child how you want to spell it, enrole them at the library and the school in any spelling you like, so by not changing it formally doesn't mean you have to stick with what you have.
After the year has past you can't change it unless through deed pole. So i'd give it careful thought as to whether it would be really worth it.
Oh and i love her name, especially pronounced with the "a" at the end. Really lovely.
Good luck.