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

Yes

The word "dois" is identical in meaning, grammar, spelling, and usage in both Brazilian and Continental Portuguese. The only differences are found in pronunciation:

• Sibilant "s": In many regions of Portugal, the "s" at the end of "dois" is pronounced as a "sh" sound ([dojs]). In much of Brazil, depending on the dialect, it is often pronounced as a sharper, dental "s" ([dois]).
• Vowel Quality: The diphthong "oi" may be articulated with slightly different openness or resonance between the two variants, but the linguistic identity of the word remains the same.

Brazilian Portuguese Examples

1. Eu quero dois cafés, por favor. (I want two coffees, please.)
2. Ele tem dois irmãos. (He has two brothers.)
3. Eu comprei dois livros ontem. (I bought two books yesterday.)
4. São dois minutos de espera. (It is two minutes of waiting.)
5. Eu tenho dois cachorros em casa. (I have two dogs at home.)

Continental Portuguese Examples

1. Quero dois cafés, por favor. (I want two coffees, please.)
2. Ele tem dois irmãos. (He has two brothers.)
3. Comprei dois livros ontem. (I bought two books yesterday.)
4. São dois minutos de espera. (It is two minutes of waiting.)
5. Eu tenho dois cães em casa. (I have two dogs at home.)