Will this relationship remain online only? That definitely makes things more challenging. How much brattiness are we talking about here? If online only, the only effective punishment I can think of is withholding rewards. Once you establish what the rewards are (an obvious one is being allowed to come) then you can withhold those as punishment or impose a time out on rewards for a number of days. Once you find out what she likes, and enjoys doing with you, other types of rewards will become evident and those can be withheld as required. But this can become a battle of wills. And it is also dependent upon your sub being somewhat obedient enough to follow these rules.
Once the dynamic is established, the extreme example of withholding is a certain level of communication from you. This can be very tricky, and potentially a slippery slope, since one of you has to give in first and the only way it will work is if it is not you. I'm not talking about cutting off communication entirely but perhaps sexting, as an example. But withholding too much too soon could damage a relationship by allowing it to wither away. So much of this is dependent upon your relationship and how it evolves, so please take this with a grain of salt. And I invite others to jump in and add their own notes since I could be giving terrible advice here!
If you intend to see each other in person periodically, a point system may be effective. Assigning points for behaviour you deem to be bratty and inflicting them as impact play in person has been an effective strategy for me in the past. After the first few in-person sessions established this dynamic, the fear of new points was an effective tool. Of course, there is a fine line between punishment and funishment! So again, this may not work in your case.
Best of luck!