Rabbit available at eatery in the country (5)

I believe the answer is:

gabon

I'm a little stuck... Click here to teach me more about this clue!

'eatery in the country' is the definition.
'gabon' can be an answer for 'country' (Gabon is an example). I am unsure of the 'eatery in the' bit.

'rabbit available' is the wordplay.
'rabbit' becomes 'gab' (I've seen this before).
'available' becomes 'on' (on can mean activated or available).
'gab'+'on'='GABON'

'at' is the link.

Can you help me to learn more?

(Other definitions for gabon that I've seen before include "French spoken here" , "African country, capital Libreville" , "West African nation" , "W. African republic" , "West African country" .)

I've seen this clue in The Independent.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.