You'll need to go from mini-DVI to HDMI (or whatever her TV has). Assuming her TV has HDMI, the easiest way to go is using a mini-DVI to DVI adaptor, and then a DVI to HDMI cable.
This will get video, but not sound. If you need sound, you can either hook up an optical cable with a 3.5mm adaptor on it, or a 3.5mm jack to RCA cable.
mini-DVI to VGA is analog, so you can't get it to work with HDMI (and wouldn't want to, since DVI converts perfectly to HDMI).
You could go the route of getting a mini-DVI to HDMI adaptor just as easily.
FWIW, technically DVI has an analog option as well, but in this case you wouldn't be using it. Just avoid any adaptors/cables that are DVI-A, stick with DVI-D or DVI-I.
It's only true on some of the brand-new Macs, but not yours. So you need a separate audio cable no matter what route you go. You could use the cable you mentioned or an optical cable since you do have optical out in your headphone jack, you just need a special adaptor.