Tegen de tijd dat de wekker morgen gaat, zal ik al wakker zijn en zal mijn broodtrommel al klaar zijn.

Yes. Tegen de tijd dat is a fixed time expression meaning by the time (that).

It introduces a point in time, and the main clause says what will already be true at that point.

So the pattern is:

tegen de tijd dat + clause, ...

For example:

• Tegen de tijd dat hij aankomt, ben ik weg.
  By the time he arrives, I’ll be gone.

Here, tegen is not being used in its basic physical sense of against. In time expressions, it often has the idea of by / around / toward a certain time.

Because Dutch normally uses the present tense in time clauses that refer to the future.

This is very similar to English:

• By the time the alarm goes off tomorrow...
• not normally by the time the alarm will go off tomorrow

So in Dutch, after expressions like als, wanneer, zodra, and tegen de tijd dat, the future event is often expressed with the present tense:

• dat de wekker morgen gaat

The future meaning is already clear from morgen and from the overall sentence.

Because dat introduces a subordinate clause, and in Dutch subordinate clauses, the finite verb usually goes to the end.

So:

• de wekker gaat morgen would be normal main-clause order
• dat de wekker morgen gaat is subordinate-clause order

That is a very common Dutch word-order rule.

This is an idiomatic use of gaan.

With things like alarms, bells, and phones, Dutch often uses gaan where English uses go off, ring, or start sounding.

So:

• De wekker gaat. = The alarm goes off.
• De telefoon gaat. = The phone is ringing.

You may also see afgaan with alarms, but de wekker gaat is completely normal and very common.

This is the future construction:

• zullen
  • infinitive

Here:

• zal = finite form of zullen
• zijn = infinitive
• wakker = complement meaning awake

So the structure is:

• zal
  • subject + rest + zijn

Why is ik after zal? Because the sentence begins with the time expression Tegen de tijd dat de wekker morgen gaat, and in a Dutch main clause the finite verb comes in second position. That causes inversion:

• Tegen de tijd dat ... zal ik ...

instead of:

• Ik zal ...

Because zullen is a modal-like auxiliary, and after it Dutch uses a bare infinitive, not te + infinitive.

So:

• zal zijn = correct
• zal te zijn = incorrect

This is the same pattern you get with other verbs like:

• kan komen
• moet werken
• wil slapen

No te is used there either.

Because they are predicate adjectives: they come after zijn and describe the subject.

In Dutch, adjectives used this way do not normally take the -e ending:

• Ik ben wakker.
• De broodtrommel is klaar.

Compare that with adjectives placed before a noun, where you often do get -e:

• de rode auto
• een grote hond

So in this sentence:

• wakker describes ik
• klaar describes mijn broodtrommel

Because this sentence has two coordinated main clauses:

• zal ik al wakker zijn
• zal mijn broodtrommel al klaar zijn

Repeating zal makes the structure parallel and clear.

It also fits the fact that the opening time phrase applies to both parts:

• Tegen de tijd dat de wekker morgen gaat,
  • zal ik al wakker zijn
  • en zal mijn broodtrommel al klaar zijn

You could also say:

• ..., en mijn broodtrommel zal al klaar zijn.

That is also possible. The version with repeated zal sounds neat and balanced.

Al means already.

It shows that both things will be true before the alarm goes off:

• ik al wakker = I’m already awake
• mijn broodtrommel al klaar = my lunchbox is already ready

Using al twice is natural because it applies separately to both clauses.

Without al, the sentence would simply say those things will be true at that time. With al, it emphasizes that they will be true by then, possibly even earlier.

Broodtrommel is a compound noun:

• brood = bread
• trommel = tin / box / container

In everyday Dutch, it usually means a lunchbox, especially one used for sandwiches.

So although the literal parts suggest something like bread box, the normal practical meaning is closer to packed lunch container or lunchbox.

Dutch often uses the present tense for future meaning when the context is clear.

So a Dutch speaker could also say something like:

• Tegen de tijd dat de wekker morgen gaat, ben ik al wakker en is mijn broodtrommel al klaar.

That is possible and natural.

Using zal here adds a clearer future flavor. It can sound a bit more deliberate, predictive, or formal. So the version in your sentence is correct, but it is not the only way Dutch can express this idea.