Police said the event happened near the junction of the A830 and A861 in the northwest Highlands at around 9.30am on Saturday.
A van taking a trip west on the A830 struck the dog and kid, with the animal pronounced dead at the scene and the driver stopping working to stop.
The kid was unscathed, officers said.
Police are now trying to find info to trace the driver, stating the van was potentially a Vauxhall with severely rusted rear doors.
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Sergeant Katy Duncan said: “Sadly, the dog did not endure its injuries. The kid was luckily unscathed however the repercussions of this accident might have been even more serious.
“We are asking anyone who might have seen this event to call authorities on 101, pricing quote referral number 1573 of July 8 2023.
“Police are likewise interesting drivers who remained in the location at this time to inspect any dashcam video footage they might have.
“Alternatively, please contact Crimestoppers anonymously on 0800 555 111.”