Actually Dirty Shoez, it does state in the Qur'an that all women are required to wear the Hijab.
Read these ayaats (verses) here:
"And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts) and not to show off their adornment except only that which is apparent (like both eyes for necessity to see the way, or outer palms of hands or one eye or dress like veil, gloves, headcover, apron), and to draw their veils all over Juyoobihinna (i.e. their bodies, faces, necks and bosoms) and not to reveal their adornment except to their husbands, or their fathers, or their husband’s fathers, or their sons, or their husband’s sons, or their brothers or their brother’s sons, or their sister’s sons, or their women (sisters in Islam)…”
[Surah Al-Noor 24:31]
O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies (i.e. screen themselves completely except the eyes or one eye to see the way). That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allaah is Ever Oft‑Forgiving, Most Merciful”
[Surah Al-Ahzaab 33:59]
And there are many ahadith where the Prophet (SAW) ordered the early Muslim women that they must wear the Hijab, and this is compulsory upon them in the presence of non-Mahram men (basically men who they're allowed to marry). Not to mention there is Ijma (consensus of the Scholars) that Hijab is obligatory upon all Muslim women who have reached the age of puberty. Like the brother said, 99% of the scholars in both the past and present hold this opinion, and they are unanimously agreed upon it. So there's no question whether it's obligatory or not.
Just do a search in google and I'm sure you'll find many articles that deal about this issue and explain thoroughly. Or better yet, you can also talk to an Imam at a local Mosque, if there's one that's close to you. They'll be glad to help you out and answer any additional questions about Islam for you.
I'm a convert too, so I know from personal experience that the people at the Masjid are very friendly and polite towards folks who want to learn more about Islam. They won't make you feel uncomfortable at all, anyone is welcome there. If you need questions like this and others answered, then don't hesistate to go to a local Mosque and talking to the Imam there, he'll be happy to help you out.
I think talking to a LEARNED person will be much more beneficial then reading a book, article, or asking one of your friends about Islam. Cause these people have much more knowledge than us, and they know how to expalin these matters in detail. Just something I recommend though, you should consider it if there's a mosque that's close to you.