OP, you're getting a hard time here, there's time to change your DD's spelling to Ellie so there's no confusion, although I must say, Elle (El) is a gorgeous name in it's own right.
My DD has a name starting El, I was determined she'd be her full name, before she'd left hospital, DH was calling her Ellie and I must say, it suits a little toddler charging around the place!
If you want to call your DD Ellie, then put that on the birth certificate. Put the other way, if she is known as Ellie, but spelt Elle, she's going to have a lifetime of correcting the spelling - I have a name witha couple of different accepted spellings, usually people get it right but I've spent a lot of time on the phone to call centres explaining that I don't have an 'i' in my name, she's going to be doing exactly the same for her whole life! People will hear Ellie and write Ellie, not Elle.
Save her the bother, put the 'i' back in.