As the following will show she hid away from the idea of giving her number, in which I am guessing I pushed at too quickly. What is the best way forward
(She sent the first message)

Her: Hi
Me: Whoa [name], slow down! Only so much you can say in one message!
Her: Lol im sorry haha
Me: lol, still more short messages! your killing me girly! we might as well text
Her: Lol im sorry !!! /.\ i cant help it haha ill right[sic] more

So she is definitely saying she'd write more, but she didn't do anything to expand, or go into the texting concept, what is the best way to proceed (I am trying out online dating for the heck of it, I do not know how to translate real life into online when it comes to the lack of physical presence)

I like how you started this... Playful and funny right from the start.
My suggestion would be to give her something to talk about. She's basically telling you to drive the conversation somewhere.
At this point I would treat it like something you're just opening. Comment and tease about something on her profile, then go from there.

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