does it have to be everyday? how about once a week, ask her how her week was and then let her tell you.
also getting to get to know her, that's why you go on dates. to get to know each other. just take it slower,I get you like her and you wanna know more but your going to come off clingy. not everyone likes that.
also as someone said the "tone" of an email. there is no tone to email or text message or anything. so don't over analysis anything.
last, do you email her when she at work? if so she may be busy with work and not have time to reply to you.
are you having any other communication with her at all? are you speaking to her on the phone? If you are not, I do find this a little odd. I especially do not like the sharpness of the tone of that last email. I also however do not disagree with the other commentors. You might be coming on a little strong to her, I do not know her so I do not know her feelings about the importance of communication in any form. Especially early on in a relationship. I am also, overly protective of you so I'm not the best gage. I'm trying to think of a reason I would ever respond to anyone with 'you really don't need to email me so much'. I can't see myself doing that unless I was actually breaking things off with someone. But...like I said I don't know her and I am not the best gage. Can you simply ask her what her preferred avenue of communication is? She will likely say in person.
Wow... she's kinda rude. How the hell are you supposed to get to know someone w/out emailing? That is the whole idea of "dating" esp. if you met online like this, you would think emailing would be a good form of communicating. :/