Ooh, baby fun! Haven't had a youngster to play with for a few years...
I haven't started training to lunge yet,
Yes, as Fox said, DON'T!! Babies are a lot more fragile than they look, when talking things like high impact exercise, weightbearing, overflexing, fighting a rope, etc. So no lunging, jumping, tying solid, letting a farrier fight with her... etc until she's close to 2yo. Well, any farrier that wants to fight a horse wouldn't be employed by me anyway, and she should be well 'broke' to lead/yield to pressure before you think about tying her firm anyway. And I'd avoid any 'real' jumping, lunging, and weightbearing/riding for a lot longer - not adverse to short, light riding, if you're a light weight & not asking much for eg, but 'real' riding I'd leave off until around 4yo and 'hard' riding, real jumping & the likes till she's around 6yo. If you don't understand the whys & wherefores about all that, study up on it. You can find good diagrams online of when certain bones & joints 'close'.
The other thing is, 'lunging' is but one small part of training, that's not actually one of the 'basics' & not even necessary. It is effectively an extension of leading/driving, only at a distance. Therefore I wouldn't be starting it even with a mature horse, until they were good at the other things, and with yielding to 'implied' signals - eg. bodylanguage & voice cues rather than actual physical pressure. And there are PLENTY of other things she should be gotten good at WAY before lunging anyway. Hoof care is one good eg. I urge you to find a good trainer to help you with this 'young lass'.
She does tie, wears a fly mask, and leads. Sorta leads.
Aside from not tying a baby 'hard' for physical reasons, I'd advise they don't just 'sorta lead' but are very good & reliable about that, and about accepting being 'tied' with a blocker tie ring or some such, well before I'd consider tying firm. You want to set her up for success.
She throws her head around and then rears. Should this behavior be corrected? I know some behaviors from young horses are written off as sort of "kids being kids"
I don't believe ANY 'bad' behaviours that you don't want to see more of should be 'written off', least of all dangerous ones such as rearing. Yes, 'kids WILL be kids' and they will test a lot of things out. But if you allow them to think saying 'pluck you Grandpa' is fine & dandy, they'll grow up to be obnoxious, disrespectful adults. And can't blame animals for not having been taught better, any more than rude kids who haven't been taught any manners. But that doesn't mean you should accept/allow it.
if this habit continues on to adulthood, I could have minor issues turn to dangerous issues.
Exactly! Nip it in the bud now, before it becomes a bigger 'monster'. And I like Fox's way of dealing with it. Whatever you do, for whatever behaviour, ensure that IF you feel the need for punishment, you punish *at the time of* the 'wrong' behaviour and effectively enough to make her think seriously before considering it again. - Better to give 'a short, sharp shock & he'll never do it again'(Pink Floyd fans - these things just come out at times!) rather than trying to give a gentle tap that's useless, or worse, she thinks is a game or an irritating 'nag' that she feels the need to punish YOU for.