Eu quero alugar um apartamento mobiliado perto do centro.

Yes. In Brazilian Portuguese, eu can often be omitted because the verb form quero already shows that the subject is I.

So both of these are natural:

• Eu quero alugar um apartamento mobiliado perto do centro.
• Quero alugar um apartamento mobiliado perto do centro.

Including eu can add emphasis, clarity, or contrast, especially if you want to stress I.

Quero is the first-person singular form of the verb querer, which means to want.

Present tense of querer:

• eu quero = I want
• você quer = you want
• ele/ela quer = he/she wants
• nós queremos = we want
• vocês querem = you all want
• eles/elas querem = they want

So eu quero means I want.

After querer, Portuguese usually uses another verb in the infinitive:

• quero alugar = I want to rent
• quero comprar = I want to buy
• quero morar = I want to live

This works much like English want + to + verb, except Portuguese does not need a separate word like to before the second verb here.

So:

• quero alugar literally corresponds to want to rent

It can mean either, depending on context.

• alugar um apartamento = to rent an apartment
• alugar meu apartamento = to rent out my apartment

In your sentence, alugar um apartamento clearly means to rent an apartment for yourself.

If you want to make the direction even clearer in some situations, Brazilian Portuguese may also use:

• alugar para morar = rent in order to live there

Um means a or one.

• um apartamento = an apartment / one apartment

In Portuguese, using the indefinite article is very common when talking about a non-specific thing. So quero alugar um apartamento sounds natural.

If you said just quero alugar apartamento, it would sound more general or less standard in this context.

Mobiliado means furnished.

So:

• apartamento mobiliado = furnished apartment

This describes an apartment that already has furniture, such as a bed, sofa, table, etc.

A useful contrast:

• mobiliado = furnished
• sem mobília / não mobiliado = unfurnished

Because mobiliado agrees with apartamento, and apartamento is a masculine singular noun.

Agreement in Portuguese:

• apartamento mobiliado = masculine singular
• casa mobiliada = feminine singular
• apartamentos mobiliados = masculine plural
• casas mobiliadas = feminine plural

So the adjective changes to match the noun it describes.

Because perto is normally followed by the preposition de:

• perto de = near

So the full structure is:

• perto de o centro

But de + o contracts to do:

• de + o = do

That is why you get:

• perto do centro

Other similar contractions:

• de + a = da
• de + os = dos
• de + as = das

Examples:

• perto da praia = near the beach
• perto dos mercados = near the markets

Because centro here is being used as a specific place: the center / downtown area.

So:

• o centro = the center, downtown
• do centro = of the center / near downtown

In Brazilian Portuguese, place expressions often use the definite article where English might not focus on it as much.

In this sentence, perto do centro is the normal way to say near downtown or near the city center.

In this context, centro usually means downtown or the city center.

So:

• perto do centro = near downtown / near the city center

The exact English translation depends on context, but in everyday Brazilian Portuguese, o centro often refers to the central commercial area of a city or neighborhood.

In Portuguese, adjectives often come after the noun.

So:

• apartamento mobiliado = furnished apartment
• carro novo = new car
• casa grande = big house

This is one of the most common word orders in Portuguese. Some adjectives can come before the noun, but after-the-noun placement is very common and natural.

You could, but um apartamento mobiliado perto do centro is clearer and more natural.

That order groups the ideas nicely:

• um apartamento mobiliado = a furnished apartment
• perto do centro = near downtown

If you move mobiliado later, the sentence may sound slightly less smooth or more ambiguous, especially in speech.

So the usual, clear version is:

• um apartamento mobiliado perto do centro

Apartamento is the full standard word and is the safest choice.

In ads, listings, and informal writing, you may also see:

• apto = abbreviation of apartamento

For example:

• Alugo apto mobiliado = I rent out a furnished apartment

But in normal speech and learning situations, apartamento is better.

You would need to change both the article and the adjective to match the feminine noun:

• Eu quero alugar uma casa mobiliada perto do centro.

Changes:

• um → uma
• mobiliado → mobiliada

This is a good example of gender agreement in Portuguese.