Historical small boats

I'm in the process of establishing a character and running into a stumbling block: my character is a sailor and I am most definitely not.

While I don't need to know too much about the actual sailing, I am having some trouble pinpointing an appropriate sort of boat for her. It's a historical fantasy setting, somewhere around 1600 but I have a fair amount of flexibility with the time period and geography this boat was really from.

It needs to be an ocean-going vessel, capable of travelling something like 800 miles between two island nations. I'd like it to be reasonably small and fast, and to have some sort of purpose - fishing probably isn't ideal, because I imagine fishing boats are pretty gross and she might end up illicitly smuggling dignitaries around. Trading or transport, maybe? Some combination?

Or is there any sort of ocean-going vessel with a reasonable chance of being crewed by one person?

I've looked at Wikipedia lists of various kinds of boat and read the entries for junk, xebec etc. I've also read back through the entire boats and sailing things tag here and seen a post asking a similar thing about a future setting. I don't quite know enough to know where to start!

Thanks in advance.