When Brazil got independent from Portugal, one of the conditions in the treaty that formally recognized the Independence (Treaty of Rio de Janeiro, signed in 1825) was that Brazil wouldn’t allow or try to make other Portuguese colonies to join it in independence. There were lots of relationships between the Brazilian colonial elite and the Portuguese African colonies elite (Angola and Mozambique) especially regarding the slave trade, and this was a true concern the Portuguese had.

Brazil wouldn’t be on the shape to try to colonize Africa in any way for quite some time, regardless of the treaty it had signed with Portugal. The independence war had left it with a very big foreign debt (2 million British pounds) and Brazil would suffer a lot of political upheavals during Pedro I’s reign and Pedro II’s regency, before he became an adult. These were some of the most turbulent times in Brazilian history, with lots of separatist movements in faraway provinces. Uruguay got its independence, but the other movements were defeated due to military victories or political mediation, but it would take all the way to 1840 (or 1848 if you count the more regional Praiera Revolution) for the situation to stabilize.

From the 1840s to the 1860s there wouldn’t be more civil war, but Brazil would focus its attention in the River Plate region, with wars and interventions in its neighbors to the South. The reason behind that was that a good chunk of Brazilian territory, the western province of Mato Grosso, for example, was accessible at that time only through moving through the Rio de La Plata (that means between Argentina and Uruguay), since there wasn’t a railroad connecting the coast to that place. So it was in Brazil’s interest to maintain sovereignty over that region to make it so that no single power controlled both margins of that river, and at the same time avoid too much instability that would infest the region with bandits that could prey on travellers going to Mato Grosso. So for that reason Brazil got involved in many wars in that region, ending with the Paraguayan War of 1864-1870, which again made the Brazilian government very indebted.

Brazil had officially abolished the importation of slaves (but not slavery) in 1826, but the law was not enforced and the illegal arrival of slaves continued unabated. This would only start to stop in 1845, when the British started to use their navy to board any ship they suspected of conducting the slave trade in the South Atlantic (Aberdeen Law). Most of those ships were Brazilians or had Brazilian crews on it, and this created a serious crisis between the two countries. Brazil was in no condition to go against the British navy regarding these things, especially as the Brazilian law was formally against the slave trade. This crisis would stop in 1852, after the 1850 Brazilian Eusebio de Queiros law, that made the Brazilian government finally enforce the slave trade ban effectively. But this law, that made the British stop to pester Brazilian ships, also took away all the incentives Brazil could have to establish colonies in Africa, which would be to get more slaves. Brazil already had much unexploited territory and resources, so what would be the reason to acquire it overseas? Also, from the “spreading Western civilization / Christianity” POV, Brazil also had many natives it didn’t contact (there are still isolated tribes today). Finally, from the 1850s to the 1880s the main question Brazil would face politically would be regarding the abolition of slavery in the country (and you can see from how this proceeded in the US that this question can consume a nation completely) and the succession of Pedro II, with many people not liking a female empress (Isabel, Pedro II’s only legitimate heir) or a foreign emperor (Count D’eu, her husband).

Edit: some Brazilians did participate in the colonization of Africa, but not as an official endeavour of the Brazilian government. Some Brazilian of African heiritage returned to Africa (with many participating in the slave trade after getting their freedom), and they formed kind of a middle strata in the colonial societies. They were Black, like the native Africans, but they had been exposed to a Western culture, and could speak Portuguese or another European language, and so the colonial administration of European powers used them as middle-mans. They were called taboms or agudas.