Why would Square give her a rod in the original... she is a magic user who is studying magic.
Actually no. In FFIV, usually a character at Lv1 means no experience whatsoever in their job including study. Rydia learned how to use magic in battle (thus starting with no spells at all outside of Chocobo), and the finer arts in the Feymarch (or whatever it's called nowadays). Seeing as how in the game typical mages in training wear the usual white/black mage robe, I'd say she was not there yet. The reason for this is as Tellah said she has great potential.
So why would Square do it? It's a gameplay choice as with most RPGs, most likely to make things easier on a first time player. Equipment costs money and they need to buy it, and someone can easily forget to put their pants on so to speak.
Really though, all of this has next to nothing to do with the situation at hand.
EDIT: Meh, getting rid of the second reply. Really chillyfeez is right, if we keep going about this wheel of anger it will end in a lock or something. This whole thing made even me go into a stupid and angry rant but really that's all it was, ranting about people being rude. No use crying about spilt milk, back to work!