I'm playing a Vampire the Masquerade dark ages game. My character, a nosferatu, has (for character specific reasons) never learned the Animalism discipline. Her ghoul however did learn it from another nosferatu at some point. My question is could her ghoul teach her the first dot of this discipline or would she require another vampire to teach her?
It would be helpful to know which edition you're refering to but I'll just answer the question in regard to the latest edition.
20th Anniversary Dark Ages, page 188:
Each clan and each bloodline shares affinity for three Disciplines. Theoretically, a Cainite may learn any Discipline with time and tutelage. She can learn the three physical Disciplines, Celerity, Fortitude, and Potence, without a teacher. She may also learn her three affinity Disciplines on her own.
So, since you are asking about an in-clan discipline: According to the rules you wouldn't need your ghoul at all - it's an in-clan discipline, you can just learn it on your own, as it's already in your blood.
Now, many GMs might houserule this or say "Learning is easier with a teacher" but going by the rules you only need a mentor who knows the Discipline if it's out-clan.
Note that this is a Dark-Ages rule, in the normal V20 the question is not addressed at all (Page 128 "Advancing Disciplines"
No, or very unlikely
@Seeamoebe is right when telling you that a vampire doesn't need a teacher to learn their in-clan Disciplines, and many GMs agree that you don't need a teacher to learn a "physical Discipline": Potence, Celerity, Fortitude. A Nosferatu character doesn't need a teacher to learn Animalism.
However, the answer to your question in the title is "No, or very unlikely", and it's located on p. 500 of the V20 Core rulebook. Look at the end of the page:
Most ghouls and revenants don’t understand the Kindred well enough to teach Disciplines to them.
And at the "I was embraced yesterday" box:
Embraced ghouls also receive the same Discipline points as a starting vampire. They retain any Disciplines learned as a ghoul when they are Embraced, including Potence. They are now also able to teach those Disciplines, to the same extent as any other vampire.
Let's say, you are in possession of a Ventrue ghoul who is able to use Dominate 1, but you can't use Dominate 1 yourself and can't learn it without a teacher, as it is not your in-clan Discipline. The ghoul can't teach it to you either -- but you really, really want to learn it, and are not willing to pay a service in exchange.
In this case you can embrace the ghoul and make them teach you Dominate 1, as they "are now also able to teach those Disciplines, to the same extent as any other vampire".
Of course, you will need to deal with the consequences of this embrace, but that's another story...