Just a little bit of clarification encryption, as I think some of the earlier comments oversimplified things a bit.
It is correct that Day One lacks encryption and stores entries as plain text. These can be read outside the App. If you are concerned about this, you can easily turn on Filevault on your Mac and set a strong login password. This way no one can read your notes except you.
On the Dropbox/iCloud side, it's really not true to say anyone can read your entries. Dropbox and iCloud both encrypt your data as soon as it leaves your computer. All data is stored on their servers in an encrypted format. Whether you trust the service or not is a separate issue, but accessing your journal entries is not trivial and certainly not achievable by 'anyone'.
If Day One added encryption, it would be a second level of security on top of the existing options - nice to have sure. But I hope the points above show the current implementation is actually pretty good security wise.
I like to try this app. Can it sync with my Calendar? Or can I transfer Calendar data to it?