Is the word doer the same in Brazilian and European Portuguese?

No

While the fundamental meaning of the verb "doer" (to ache or to hurt) is identical in both dialects, there are significant differences in typical usage regarding its conjugation and how it interacts with other parts of a sentence.

• Grammatical Construction (Aspect): In Brazilian Portuguese, when expressing an ongoing sensation of pain, the gerund is the standard usage (e.g., está doendo). In Continental Portuguese, the construction a + infinitive is used instead (e.g., está a doer).
• Clitic Placement: When the verb is used with an object pronoun (e.g., "it hurts me"), Brazilians typically use proclisis (me dói), whereas Portuguese people typically use enclisis (dói-me).
• Pronunciation: In Brazilian Portuguese, the vowels in "doer" are generally more open and the "e" is clearly articulated. In Continental Portuguese, there is significant vowel reduction, often making the "e" much shorter or more closed.

Brazilian Portuguese Examples

1. Minha cabeça está doendo muito. (My head is hurting a lot.)
2. Me dói ver você triste assim. (It hurts me to see you sad like this.)
3. O meu pé está doendo depois da corrida. (My foot is hurting after the run.)
4. A garganta está doendo bastante hoje. (The throat is hurting quite a bit today.)
5. Isso vai doer muito, eu te aviso. (This is going to hurt a lot, I'm warning you.)

Continental Portuguese Examples

1. A minha cabeça está a doer muito. (My head is hurting a lot.)
2. Dói-me ver-te triste assim. (It hurts me to see you sad like this.)
3. O meu pé está a doer depois da corrida. (My foot is hurting after the run.)
4. A garganta está a doer bastante hoje. (The throat is hurting quite a bit today.)
5. Isto vai doer muito, eu aviso-te. (This is going to hurt a lot, I'm warning you.)