I guess it really depends on whether you'd like people to pronounce it gabi (like gah-bee) or gabby (like gab-bee) Because that's how I would personally pronounce those spellings.
You will have to spell it out on certain occasions.
We've called my oldest and middle children by their nicknames and all their gifts come with that name on the tag. There is also the fact that some longer names are harder for little ones to spell out and you might want your daughter to go by her nickname in school. (Their names are the first words that they learn to spell usually)
My oldest is in 1st grade now and although she can spell her full first name (Victoria) it was much easier for everyone in earlier times because we called her Torri.
In the same way, my 3-year-old's name is Galatea and we have all KINDS of problems with her name. Her nick-name is Teya, with the 'y' placed in so that people don't accidently call her tea (as in the beverage).
Either way, you're the mom, so your word is law! Don't let anyone give you trouble about the spelling of your daughter's name!