You can get the bounds of the text box using the stringFT() method, but you will need to load up a truetype font first - see the "Character and String Drawing" section in the GD docs.
According to GD#Font-Utilities, gdGiantFont is a fixed width (monospace) 9x15 font, so unless I'm very much mistaken, it's just 9*nChars to get the width, and the height is a fixed 15 per line of text.
edit and it's got the width and height methods to tell you those numbers in the code.