Online & Apps Asking for a girl's number through OL Chat

[Astigmatic20]

I recently chatted online with this cute girl who I haven't met in a long time. I proposed to her that we should go out and she asked me when and where we'll meet. As much as possible, I'd rather ask for her schedule through text so I asked for her number. She told me that she'll just get my number since her phone is lost somewhere in her room. I didn't cave at first to avoid a flake move in her part so I told her to tell me her number to save her the trouble of looking for her phone. She then replied that she didn't memorize it. I persisted and told her something along the lines of "You're a smart girl, I know you memorized it" but she replied that it was a new phone so she didn't memorize her number yet. I ended up giving her number so I wouldn't come off as annoying in getting her number. However, I did tell her to text me asap when she'll be free next week since I've been busy lately.

With that said, did I end up doing a wrong move in giving her my number instead? Also, in similar situations, what would be the best way to ask for a girl's number through online chat?