Is a framed drawing a good birthday gift for a friend that I’ve only known for a short period of time?

It’s a lovely gift. No need to worry.

It does sound lovely, as @janbb says. But your hesitation is telling. If you are feeling that it might be an inappropriately special gift, as if it represented a closer relationship than you actually have, your doubt may be giving you good advice. Perhaps choose something a little less personal, or even just omit the frame?

I’d just downplay how much effort went into it, and I might skip the frame (maybe double-sided tape onto matboard)?

“Hey [her name], I hope you don’t think I’m too cheap to get you a real present, but I know you’re into Asian stuff, so I scribbled a little something for you. Hope you like it. Happy birthday.” You could also give it a funny title to tone it down: “Pen and Ink: Asian Bear Eating Asian Stick #1”

I forgot to mention that she’s moving to Thailand for about a year. So that’s what really sparked my idea for a going away present.

I like the idea assuming it’s not very large. I’d love to receive a sketch or painting from a friend that depicts something I like or am interested in.

Are most people giving inexpensive token gifts? She can always use the frame for a favorite photo, or regift the frame if moving with it is a burden and put your drawing in with other papers she has.

That sounds like a very wonderful, thoughtful gift. I personally would love receiving such a gift.

Apparently you’re confident enough about your artistic ability, so I would give the sketch, framed or unframed, with confidence if I were you.

I think it’s great! Very cool.

Update?

Oooo I’d love something like that and would be flattered that you knew enough about me to do that. People like feeling special.

She loved the drawing! And another friend in our group made her a crochet hat, so I wasn’t the only one that gave her a handmade gift, which was nice.

Yayyyy! Glad it worked out! Thanks for letting us know.