Hun er begyndt at kravle rundt i børneværelset om morgenen.

It is the present perfect.

• er = present tense of være (to be)
• begyndt = past participle of begynde (to begin / to start)

So Hun er begyndt ... means She has started ...

This tense is used when the action began in the past but is relevant now. In this sentence, it suggests that crawling around in the children’s room is a new development.

In Danish, some verbs—especially intransitive verbs involving change of state or movement—can use være as the auxiliary in the perfect tense.

With begynde in a sentence like this, er begyndt at ... is the normal pattern learners should use:

• Hun er begyndt at kravle = She has started crawling

So even though English says has started, Danish often says is begun/has begun with er here.

Because after begynde when another verb follows, Danish normally uses at + infinitive.

So:

• begynde at kravle = to start crawling
• begynde at spise = to start eating
• begynde at græde = to start crying

Here:

• kravle is the infinitive
• at is the infinitive marker, like English to

kravle means to crawl.

rundt adds the idea of moving around rather than just crawling in one direction.

So:

• kravle = crawl
• kravle rundt = crawl around

It sounds natural if you are describing a baby or small child moving around a room.

Because i børneværelset means in the children’s room—inside it.

• rundt i børneværelset = around in the children’s room
• rundt om børneværelset would suggest movement around the room as an object, more like around it from the outside or around its edges

So in this sentence, rundt is enough for around, and i børneværelset gives the location.

It is a compound noun:

• børne- = child / children-related
• værelse = room
• -t / -et as part of værelset = the definite ending

So:

• et børneværelse = a children’s room / a nursery
• børneværelset = the children’s room / the nursery

A useful thing to notice is that Danish often builds long nouns by combining smaller parts.

Because Danish usually puts the definite article at the end of the noun instead of using a separate word in front.

Compare:

• et værelse = a room
• værelset = the room

So:

• et børneværelse = a children’s room
• børneværelset = the children’s room

That is why you do not need a separate word like English the here.

Because i is the normal preposition for being inside an enclosed space such as a room.

• i værelset = in the room
• i huset = in the house
• i bilen = in the car

So i børneværelset simply means in the children’s room.

It means in the morning or in the mornings.

In this sentence, it most naturally suggests a habit or repeated time:

• Hun er begyndt at kravle rundt i børneværelset om morgenen
  = She has started crawling around in the children’s room in the morning / in the mornings

Because the sentence uses has started, it suggests that this morning behavior is something new.

Because the two expressions mean different things.

• om morgenen = in the morning / in the mornings, general or habitual
• i morges = this morning, one specific morning

So if you mean a new routine or general behavior, om morgenen fits.

If you said:

• Hun kravlede rundt i børneværelset i morges

that would mean:

• She crawled around in the children’s room this morning

That is a specific event, not a general morning habit.

Because after om in expressions like this, Danish often uses the definite form.

Common examples:

• om morgenen = in the morning
• om aftenen = in the evening
• om natten = at night

This is just the normal idiomatic pattern, so it is best to learn it as a set expression.

Yes, but Danish follows the V2 rule in main clauses: the finite verb must come in the second position.

In the original sentence:

• Hun = first element
• er = second element

So the sentence begins:

• Hun er ...

If you move the time phrase to the front, the verb still has to stay second:

• Om morgenen er hun begyndt at kravle rundt i børneværelset.

That is grammatical, but it gives extra emphasis to om morgenen. The original version is a very natural neutral order.