Hi there,

Slugs are not poisonous to dog.

To be very thorough, and probably over the top...in the future...

If your dog develops a chronic cough - you should consider lungworm infection.

Technically, although again - rare and over the top - Slugs can transmit lung worms...

Please let me know if you have other questions!
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The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would highly advise contacting your regular veterinarian.