You've run afoul of the most common problem with new players and spellcasters: unfamiliarity with the spell list. It's true that a lot of players in this situation simply want a character who can "make magic" and don't really have the "book learning" aspect in mind. Some, however, do, and I agree you certainly don't want the player discarding or changing character concept in midstream.
At level 6, the character probably doesn't (and a new player shouldn't!) have *that* many spells. Have you suggested/prepared a spell "cheat sheet" for this player? Such a sheet might include the "one liners" from the PHB spell list (only for the spells the character knows), and a few blank boxes next to each to record preparation/expenditure. Such sheets can be useful for any spellcaster, not just wizards played by new players.
How about a quick copy/paste job from the SRD, to give the player a customized "spellbook"? One or two spells per page should result in plenty of white space so the player can take notes if so inclined. "Very Useful" or "Rarely Useful," that kind of thing. Many players dislike the idea of "studying" (working) to more effectively play their characters (have fun), but you might suggest this as well.
If keeping the wizard, this player may be in need of some advice regarding daily spell preparation. I get the impression (though please feel free to correct me) that this player feels a little lost in all the options available. A little guidance might be in order here, though as noted it's important to always let the player make the final decisions for her character.
If making the switch from wizard to sorcerer, consider making the "leftover" spells available as scrolls: the character can still use them (once each) at any time, and replacing the scrolls could become an issue if one or more of them are particularly useful (though of course the *really* useful spells should end up in the sorcerer's Spells Known list).
A more radical approach might be to keep the character a wizard but remove the need for daily preparation. Because this combines the best feature of the sorcerer with the versatility of the wizard, it will probably end up making the party a bit more powerful, especially if you institute this for the druid as well. The only remaining differences between the wizard and sorcerer will be the size of the spellbook, number of spells/day, and number and use of metamagic feats. If all that is okay with you, consider giving this variant a test drive. It worked quite well for me in 2E....
EDIT: StalkingBlue's pre-fab spell prep lists are an excellent idea. I also second the sentiment that it seems as though the other players are being awfully harsh to the new player. IME, elf spellcasters are fairly common choices for new players for some reason. We're all here to have a fun, positive experience after all.
