This is the HMS Ariel that Jack Aubrey commands in The Surgeon's Mate. In the book, the Ariel is described as a "frigate in miniature," which indeed she appears to be. The Ariel is a 16-gun ship-rigged sloop of war, sloop meaning she is intended to be commanded by a lieutenant, rather than a post captain. There was a real life sloop HMS Ariel, though, unlike in the book, she was built in England, not captured from the French. She mounted 16 six-pounder long guns, and six twelve-pounder carronades.

Additional Notes

I apologize for the small space inside the ship; due to the short length and narrow beam, moving around inside may be somewhat difficult, but it was the best that I could do.