The earth is currently about 4.55 Billion years old. The year 10,000 has already passed so the answer is yes.

If you mean the year 10,000 C.E which is about 8,000 years from now, the answer is also yes. The chances that the planet will not survive another 8,000 years are infinitesimally small. 8,000 years is 2.4 x 10^4% of the lifespan of the earth, a very small amount of time on the geological time scale. The chances humanity will survive another 8,000 are open to debate but probably high, we are a resilient and resourceful bunch.
Source(s):
http://www.talkorigins.org

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If your question is whether the actual planet will survive another 8,000 years or so, then yes, I don't think it will be destroyed by meteor or something else.

Or something like this:
http://www.youtube.com/watch?v=nZMwKPmsbWE

If you are asking whether humans will be around until 10,000 A.D., then yes. We will continue being human, that is, creating technologies that have the potential to destroy us (nuclear weapons, biological weapons, climate change, etc), but I also think we will continue to advance the technologies required to keep us safe and living.
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