I'm having some confusion about word order when using the copula.
For instance:

Is fear mé == I am a man

me is the second noun in Irish, and I is the first noun in Irish

Is í an bhean mo dochtúir == ??

Now, does that second example mean "The woman is my doctor" or does it mean "My doctor is the woman"??

It means "The woman is my doctor". But actually, it doesn't make much difference.
If you say "the woman = my doctor" or "my doctor = the woman", it's the same thing.

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Agus is í Gaeilg Ġaoṫ Doḃair is binne

As Lughaidh said, there's no real difference between "The woman is my doctor" and "My doctor is the woman"...even in English. You could say that the first sentence emphasizes "woman" and the second emphasizes "my," but the basic meaning is the same.

As far as word order goes, the pronoun goes directly after the copula when the noun is definite. If not, it goes at the end. So:

Is bean mé: I am a woman

Is mise an bhean: I am the woman.

Is dochtúir í: She is a doctor

Is í an dochtúir: She is the doctor

An dochtúir thú?: Are you a doctor?

An tusa an dochtúir?: Are you the doctor?

"Me" and "I" are both represented by "mé" in Irish. And they are pronouns. Not quite sure what you mean by the "first noun" and the "second noun."

Redwolf

It can mean both.

Usually, the predicate is first, the subject second in an Irish copula sentence. In an English sentence the subject is first.
So, "Is í an bhean mo dhochtúir" = "My doctor is the woman". (so I have to disagree with Lughaidh)

But it depends on context.
If someone asks "Cé hé do dhochtúir?" And you say "Is í an bhean mo dhochtúir" it means "My doctor is the woman".
If someone asks "Cé hí an bhean?" And you say "Is í an bhean mo dhochtúir" it means "The woman is my doctor".

In the last instance a little stop (-) is made before the predicate in the spoken language: "Is í an bhean - mo dhochtúir"
(acc. to Graiméar Gaeilge na mBráithre Críostaí, 16.39)

actually I think you are right

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Just pointing it out, but in the other dialects outside Donegal (and the standard), it'd be is í an dochtúir í.

In Donegal, people also say "Is í an doctúr í", they don't drop the final í as far as I know.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Thanks guys. It was that bit about word order being determined by whether or not the noun is definite that I was missing.

I don't think I've ever heard it used.

Redwolf

I don't think I've ever heard "Is í an dochtúir: She is the doctor" either. And they don't even say "dochtúir" in Donegal... they say "doctúr" pronounced "doctar" (just like "gasúr" is pronounced "gasar").

_________________
Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne