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The child will require his or her own residence permit. See Child born in the Netherlands on the website of the Dutch IND for information about how to apply.
However, if you travel to Germany or Austria without a residence permit, you are unlikely to receive much worse than a warning if this comes to the attention of government authorities. In the worst case, you will probably be liable to pay a fine.
If you will be flying, you should check with the airlines to see whether they will require proof of immigration status for your child.