Dutch is a Germanic language, while Spanish and Portuguese are Romance languages. They shouldn't have noticeably similar roots today, but there could be loan words resulting as cultures encountered one another. The Netherlands used to be a Spanish territory during the Age of Exploration, so there probably is a connection.
Seemingly it's French loanword: https://en.wiktionary.org/wiki/konijn. Looking up etymologies for the English word "coney" it's apparently of Iberian (pre-Roman colonization origin), so likely Celtic (or from a predecessor of modern Basque). Although the modern Irish word "coinín" apparently also originates as a French loan.
In other sentece, i used 'het olifant' and that 'het' was wrong, so 'de' was right... In comments, someone wrote a link and, after i read it, i thought a singular animal was treated as a male o female (not even children). But in this case, 'het konijn' is a right sentence...