Vim move cursor one character in insert mode without arrow keys

Map ) to skip over the exisiting ) if it is a closing parenthesis

inoremap <expr> )  strpart(getline('.'), col('.')-1, 1) == ")" ? "\<Right>" : ")"

Taken from: http://vim.wikia.com/wiki/Automatically_append_closing_characters

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Old Answer

:h i_CTRL-O execute one command, return to Insert mode.

Ctrl-ol will move you one character to the right then return you to insert mode.

Alternatively some of the bracket plugins allow you to just type the closing bracket ) and they will override the existing one.