If "I wonder" is separated by a comma, should the sentence end in a question mark instead of a full stop?

Yes, the sentence is correct. It is correct because "I wonder" is being used as an "introductory phrase"

An inroductory phrase is a group of words that comes before the main clause in a sentence. It helps the reader understand more about the main clause.

• I wonder, is it time for breakfast?

Would work as a correct sentence without the introductory phrase

• Is it time for breakfast?

Some introductory phrases that are commonly used include

• While driving, I noticed a new shop on Main Street.
• During breakfast, the house lost power.
• After school, the students gathered in the library to study.

Each one of these examples could be altered to make the phrase a component of the sentence without it being part of an introductory phrase. In some cases, very short introductory phrases might not even require a seperating comma, but those cases are rare. Typically a comma is used.

• Thinking quickly he grabbed his coat.

Which I prefer

• Thinking quickly, he grabbed his coat.

https://grammar.yourdictionary.com/using-introductory-phrases-correctly.html

I wonder if it's time for breakfast. [most usual, no comma]

Is it time for breakfast, I wonder? [comma, the wondering is an afterthought]

That's really two sentences or, at least two separate thoughts, rather than one (although you could make them into a single sentence by connecting them with whether and adjusting the word order slighly.)

The question is really just about how to punctuate them. The comma isn't ideal, as it denotes a pause or separation in one sentence.

I would suggest a semi-colon, which is used to connect two related ideas. It's somewhere between a comma and a full stop (period):

I wonder; is it time for breakfast?

or, an exclamation mark:

I wonder! Is it time for breakfast?

or possibly a dash (although many might frown on this as lazy)

I wonder - is it time for breakfast?

https://www.thepunctuationguide.com/semicolon.html
http://www.sussex.ac.uk/informatics/punctuation/