Both are OK.

The first is more neutral, detached.

The 2nd shows perhaps what you're thinking right now, it's more implicated/involved. You're giving access to the listener to your inner thoughts at the time.

However, this is to over-analyze. Many people would use them alternately.

Both show up in published books:

20 on "I plan to study law"

4 on "I'm planning to study law"
My half-penny:

It's usually considered better grammatical form to respond by using the same form as in the question.

Since Speaker A used the simple present, I'd expect Speaker B to do likewise:

A: What do you plan to do after graduation?
B: I plan to study abroad.

A: What are you planning to do after graduation?
B: I'm planning to study abroad.

There's no hard-and-fast rule about this; it's just considered better form.

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