Was Minerva McGonagall an unregistered animagus in 1981?

Question

"How did you know it was me?"

This is what Minerva says when Dumbledore reveals that he knows she was there...

"Fancy seeing you here, Professor McGonagall." … She looked distinctly ruffled.

She shouldn't have been so surprised if she was registered, now would she?

Yes, I know she was registered when Hermione checked, but that was a decade later.

Was Minerva McGonagall an unregistered animagus in 1981?

Answer 1

She was used to being unrecognized in her cat form

As noted by Gallifreyan, the Pottermore article clearly states that she was registered before she graduated Hogwarts, and with Dumbledore's help.

By the end of her education at Hogwarts, Minerva McGonagall had achieved an impressive record: top grades in O.W.L.s and N.E.W.T.s, Prefect, Head Girl, and winner of the Transfiguration Today Most Promising Newcomer award. Under the guidance of her inspirational Transfiguration teacher, Albus Dumbledore, she had managed to become an Animagus; her animal form, with its distinctive markings (tabby cat, square spectacles markings around the eyes) were duly logged into the Ministry of Magic's Animagus Registry.
_{Pottermore - Professor McGonagall}

So why was she surprised? Because she was used to using that form to pass completely unnoticed by all except her the Aurors she worked with. Although she was close with Dumbledore, she wasn't working for the Order at the time.

Minerva McGonagall did not teach the young Tom Riddle, but she was privy to Dumbledore’s fears and suspicions about him. Minerva was not inducted into the Order of the Phoenix during Voldemort’s first climb to power (at that time the Order of the Phoenix was seen as a renegade outfit by the Ministry; successive Ministers feared Dumbledore’s charisma and magical talent, and were inclined to harbour fears that he wished to succeed them). Minerva’s abilities as an Animagus were to prove useful in these dark periods of wizarding history, however, and unbeknownst to her students she spent many nights spying for the Ministry in the guise of a tabby cat, bringing the Aurors crucial information on the activities of Voldemort’s followers.
_{Pottermore - Professor McGonagall (behind paywall)}

Answer 2

From Pottermore (by J.K. Rowling):

Under the guidance of her inspirational Transfiguration teacher, Albus Dumbledore, she had managed to become an Animagus; her animal form, with its distinctive markings (tabby cat, square spectacles markings around eyes) were duly logged in the Ministry of Magic’s Animagus Registry.

_{Emphasis mine}

While this doesn't have a date stamp on it, it is implied that her being an Animagus was logged right after she completed her training as one.

From a related question, we see that Dumbledore did not know that McGonagall was going to be at Privet Drive. To combine this with The Dark Lord's comment, we can conjecture that McGonagall was surprised because she thought Dumbledore had no way of knowing she would be waiting there, let alone recognize her in her cat form. Dumbledore, of course, being very observant, easily recognized his former student.

Answer 3

We see throughout a few of the books that Dumbledore seems to know quite a lot about what normal people would never perceive.

Considering the many inventions he created, and how great a wizard he was, I think there are multiple possibilities as to why he would have known she was there, beyond just, "he recognized his student".

In fact, I think that makes her surprise all the much more interesting. Perhaps she thought better of her own abilities and underestimated his? Perhaps Dumbledore hadn't had as many accomplishments back then? (unlikely)

I think the better explanation is that JK wanted to just give her some character in the way she spoke to Albus, and show they were on very close terms.