Dóttir mín er á leikskóla í dag.

In Icelandic, possessive words like mín often come after the noun in a neutral, everyday style:

• dóttir mín = my daughter

The version mín dóttir is also possible, but it often sounds more emphatic, contrastive, or sometimes a bit more literary. So for a simple statement, dóttir mín is very natural.

Because Icelandic possessives must agree with the noun they describe in gender, number, and case.

dóttir is:

• feminine
• singular
• nominative here

So the correct form is mín.

Compare:

• minn for masculine singular
• mín for feminine singular
• mitt for neuter singular

So:

• sonur minn = my son
• dóttir mín = my daughter
• barn mitt = my child

Dóttir is in the nominative singular because it is the subject of the sentence.

The sentence structure is:

• Dóttir mín = subject
• er = verb
• á leikskóla = location/state
• í dag = time expression

In Icelandic, the subject of a normal sentence like this is usually in the nominative.

Er is the 3rd person singular present tense of the verb vera = to be.

So here:

• er = is

That matches the singular subject dóttir mín.

Some forms of vera:

• ég er = I am
• þú ert = you are
• hann / hún / það er = he / she / it is

This is mostly something you have to learn as part of the expression. Icelandic prepositions often do not match English prepositions one-for-one.

With leikskóli (preschool / kindergarten), Icelandic commonly says:

• á leikskóla

even though English might say:

• at preschool
• in preschool
• at kindergarten

So á here should not be understood literally as on. It is just the normal Icelandic preposition in this expression.

Here it is best understood as dative singular, because á normally takes the dative when it shows location rather than movement.

Since the sentence says:

• Dóttir mín er ... = My daughter is ...

this is a location/state meaning, not movement.

A useful extra point: with the noun leikskóli, the singular accusative and dative forms are both leikskóla, so the form looks the same either way. That is why you cannot tell the case just by looking at the ending here.

There are two reasons:

1. Icelandic has no separate word for the indefinite article
   So there is no exact word like English a.

2. Institutional expressions often appear without the definite article
   In phrases like á leikskóla, the noun can be used in a general institutional sense, similar to English at school.

Also, Icelandic usually expresses the with a suffix on the noun, not a separate word. So:

• leikskóli = preschool / a preschool
• leikskólinn = the preschool

And in other cases:

• á leikskólanum = at the preschool

So á leikskóla is more general, while á leikskólanum points more clearly to a specific preschool.

Í dag literally means in day, but as a fixed expression it means today.

This is a very common Icelandic time phrase:

• í dag = today
• á morgun = tomorrow
• í gær = yesterday

So in this sentence, í dag simply tells you when the situation is true.

Yes. Icelandic word order is fairly flexible, especially with time expressions.

Your sentence:

• Dóttir mín er á leikskóla í dag.

A very natural alternative is:

• Í dag er dóttir mín á leikskóla.

When a time phrase like Í dag comes first, Icelandic normally keeps the verb in second position:

• Í dag
  • er
    • dóttir mín ...

That verb-second pattern is very important in Icelandic main clauses.

It can often be translated either way in natural English, depending on context.

English might say:

• My daughter is at preschool today
• My daughter is in preschool today

The Icelandic phrase does not map perfectly onto just one English preposition. The important thing is that á leikskóla is the normal Icelandic way to express that idea.