As a PhD student, should I give a talk at a conference outside my supervisor's field?
As @eykanal stated, the answer is simply to talk to your supervisor.

To specifically answer your questions:

1- Yes, it is more than OK to go to the conference. Being invited to an international conference is a great achievement that you should be proud of.

2- I don't see how it could be unethical to your supervisor.

I'm not sure from your question if your advisor has already refused the funds. I would suggest to not overthink this. Budget are generally tight. If your supervisor is a normal human being (most are), he's probably proud of your achievement. If for some reasons he doesn't approve, but does not clearly forbid you to go...well that's a strange situation but you can't guess his mind, can't you? If your relation is good, discussing is the only way to know.

Just remember that the goal of the PhD is to create an independent researcher out of you. Not a duplicate of your supervisor.