Q:

As a Brazilian pilot, can I buy an aircraft in the US then fly it to Brazil to register it?

I have a pilot license in Brazil and would like to purchase an aircraft in the US and then register it in my country.
My license allows me to fly the aircraft back to my country?

A:

I'm not sure if you're asking about general export regulations, in which case Farhan's link is useful, or the more specific licensing question.
But regarding licensing it's clear that you may not fly a US aircraft from the US to Brazil with only a Brazilian license. 14 CFR 61.3 says:

(a) Required pilot certificate for operating a civil aircraft of the
  United States. No person may serve as a required pilot flight
  crewmember of a civil aircraft of the United States, unless that
  person:
(1) Has in the person's physical possession or readily accessible in
  the aircraft when exercising the privileges of that pilot certificate
  or authorization—
(i) A pilot certificate issued under this part and in accordance with
  §61.19;
(ii) A special purpose pilot authorization issued under §61.77;
(iii) A temporary certificate issued under §61.17;
(iv) A document conveying temporary authority to exercise certificate
  privileges issued by the Airmen Certification Branch under §61.29(e);
  or
(v) When operating an aircraft within a foreign country, a pilot
  license issued by that country may be used.

In other words, you can use your Brazilian license to fly a US aircraft in Brazil (see 61.3(a)(1)(v) above) but otherwise you need a US license or a special authorization (61.77 covers leasing and commercial operations so it almost certainly won't apply to you).
I know very little about this, but at least in theory it looks like your options are:

Get a US license yourself, perhaps a foreign-based license based on your Brazilian one (see 61.75)
Get some special permission from the FAA
Pay a ferry company to fly or transport the aircraft to Brazil
Register the aircraft as Brazilian before it leaves the US (this may not even be possible)

And those are only the FAA/aviation issues, you have to think about customs and general import/export regulations too, both in the US and Brazil. I would look for some specialized help with this.

