A half-uncial G (which looks a little bit like S in Roman type) would be correct.
In Gaelic type upper and lower case are generally distinguished only by the size of the letter (upper case letters are bigger than lower case letters). Only R and S have distinct upper and lower case forms.
A dot over a letter means that it is lenited and is equivalent to a following H in Roman type (Ḃ = BH, Ċ = CH, Ḋ = DH, Ḟ = FH, Ġ = GH, etc.); this only occurs at the beginning of names in certain grammatically conditioned contexts, such as in the vocative or genitive cases, so it probably isn't what you're looking for.
Duibhlinn and Ceanannas are both good Gaelic fonts (Duibhlinn is the "classic" Gaelic font, while Ceanannas is based on the script used in the Book of Kells).
By the way, the name Gavin is usually gaelicised as Gábhán.