It's a fine line. If it looks like you are trying to buy her or her company she will know this and take the drink you bought her back to her mates. I tend to avoid buying drinks for girls for this reason. On the other hand if you've established good vibes with her - like K probably did - then sure thing.

And yeah, like you say Adam. It's nice to reward her for coming into the venue with you. It's more a common courtesy at this stage.