Your partner can apply for an EEA family permit. It's not necessary, however, because your partner, being a Brazilian citizen, is eligible to enter the UK without a visa.
The advantage of the EEA family permit is that it allows you to get an official evaluation of all your documents before you travel to the UK -- without one, you would present these documents at the border, and while the risk of rejection is low, the associated cost is much higher if you're applying for entry at the border. In addition, the EEA family permit is free of charge.
The EEA family permit regime is the UK's implementation of European Union directive 2004/38/EC. The rules are therefore likely to change at some point in the next two or three years as the UK works out the implications of the "Brexit" referendum. There's a significant chance that the UK will leave the freedom-of-movement regime, since immigration was a major issue in the referendum.
I asked in a comment whether your partnership is officially registered. That makes a difference because, if it is, your partner falls under the official definition of "family member," from Article 2, paragraph (2)(b). However, as I re-read the paragraph, it seems that registration only counts if it is done in a "member state":
the partner with whom the Union citizen has contracted a registered partnership, on the basis of the legislation of a Member State, if the legislation of the host Member State treats registered partnerships as equivalent to marriage and in accordance with the conditions laid down in the relevant legislation of the host Member State;
So under EU law, if your partnership is registered in Brazil, the UK may not be required to recognize it, though the UK may choose to recognize it anyway. It seems perhaps that this is the case, since their own guidance says simply that "civil partners" are eligible:
Qualifying as a family member
You must be the EEA citizen’s spouse or civil partner, or [...]
Even if your partnership is not officially registered, however, you ought to be able to qualify as an "extended family member or unmarried partner." From the EU directive, Article 3, paragraph (2)(b):
Without prejudice to any right to free movement and residence the persons concerned may have in their own right, the host Member State shall, in accordance with its national legislation, facilitate entry and residence for the following persons:
(b) the partner with whom the Union citizen has a durable relationship, duly attested.
And, from the UK guidance:
Qualifying as an extended family member or unmarried partner
You can also apply as an unmarried partner if you can show that you’re in a lasting relationship with the EEA national.
The difference here is that if you have registration documents, you are generally relieved of the requirement to show that your relationship is genuine; in that case, you should only be required to offer evidence of a genuine relationship if the visa officer can demonstrate a suspicion that yours is a civil partnership "of convenience." This might reasonably happen if your partnership was registered recently, but if you registered soon after beginning to live together four years ago, it is far less likely.