I dislike it and would prefer to see Gianna, Johnna / Johna, Joan, Joanna, Joanne, Jana, Johanna, Johana... The list goes on and on.
Oops! Forgot middles...
Nothing spectacular but I think Violet balances it well.
Johnni and one of my friend's former mentor was named Johnna...and I know a Jonna myself.
I can't say I partically care for it, but I suppose it could be worse. It's just when you hear "Johnny!!!!", you picture a little boy, and with so many spelling variations that are used nowadays, I would think that Johnni could be/could be mistaken for either a boy or a girl. The boys' nn Johnny honestly sounds sweetly soft itself as well. Could be confusing. That being said, the Johnni I went to school with frequently had problems with teachers/subs taking attendance and automatically looking for a boy to raise his hand. I really think the sentiment behind situations like you mentioned (little girl being named after dad) is sweet, but in this case, I would prefer Johnna/Jonna.
I think that a really feminine or at least an unmistakingly female name would work best as a nn.
....something along those lines perhaps?
Jonni (pronounced Johnny) is not my style for a girl. If I were going to try to honor a John that way, I would use Joni (pronounced Joan- ee) as in Joni Mitchell. That said with Jonni, as with any unisex girls first name, I would use a very feminine middle name. In this case, I would also go with a classic name.