I'd suggest something similar to @Ælis' answer. However, I'd phrase it like:
You: I'm going to be in London for the big Poké event!
Her: Omgggg. Really?
... (Poké discussion here)
You: While I'm there, I'm planning to get trinkets for a bunch of my friends. Would you want me to get you one too?
Similar to Ælis, this focuses on asking permission. But this response has a couple layers.
By mentioning you're already buying a bunch for your friends, you avoid singling her out. By using the word "trinket" in conjunction with the fact that you're buying many, you imply that the gift will be relatively small and cheap. And lastly and most importantly, you're making it easy for her to assert her boundaries and say no.
You're correct to worry about asking for her address as that is a big boundary. However, by asking, you make it easy for her to say no without making things awkward. Here she could simply say "Oh that's a nice thought, but [simple excuse]. Maybe next time!" and there'd be barely a hiccup in the friendship.
On the other hand, if she does say yes, I wouldn't follow up with "Okay, give me your address." Instead, I'd again let her set the boundaries. Maybe saying something like:
Awesome! How did you want me to get that to you?
Maybe she'll just give you her address. Maybe she has some third party vendor where you can drop off the gift with a tracking number and then she'll never have to give you her address at all. Who knows! But the point here is--again--to leave the ball in her court and make it easy to assert her boundaries and say no without making things awkward. You're making no assumptions.
As a side note, this is something I wish I'd done with one of my online friends. After we'd been talking for awhile, I happened to be taking a trip to his neck of the woods (for unrelated reasons) and sprung it on him. I hoped that we could hangout and meet in person and already found a dinner place and everything. I was so excited to surprise him, but when I did, he got extremely awkward about it. He was uncomfortable with the idea of meeting in person alone and felt it was all so last minute. Suffice to say, if I'd approached him without making assumptions and focused on making it easy for him to say no at any point in the planning, I think we both would've felt more comfortable.