Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern for Dexter but, fortunately, dogs tend to tolerate opioids of this sort fairly well. At this dose you might see sedation or balance issues but not much more than this.
If Dexter ingested the Oxycodone < 1 hour ago, you could induce vomiting if you have fresh 3% hydrogen peroxide (it should bubble and fizz); The dose would be 1 teaspoon mixed with bread, walk him around and repeat the dosage in 15 minutes. Not all dogs will vomit when peroxide is given but most will.
If more time has elapsed, most of the drug is probably already absorbed. If that's the case, then monitor for about 4 hrs to see how sedate he becomes; if this behavior does develop, then keep him confined and away from obstacles to avoid accidental injury.
More than likely, he'll be fine such that an ER visit is not required.
I hope this helps to reassure you about him. Deb