No, that's the wrong order.

The indirect object pronoun comes between the verb and the direct object in English, not the other way around. You give the baby a bath; you never give a bath the baby, because that would be something else. Ordering matters in English.

In German you can tell that mir is dative (indirect object) not accusative (direct object, which would be mich)

Not here. English has lost all distinction in casing for the different sorts of objects. So these become forbidden in (American?) English.

  • Send her the document.
  • *Send the document her. [WRONG]

The problem is that a direct object pronoun needs to immediately follow the verb, which pushes the indirect object away. You can’t have both an indirect and direct object pronoun. You have to convert the indirect object into a trailing prepositional phrase instead.

  • *Send her it. [WRONG]
  • *Send it her. [WRONG]
  • Send it to her.