Is full stop needed?

no, the period is incorrect...

Any idea whether it is different in British English.

A full stop would be necessary after the quotation marks if the quotation finishes a sentence like it does in this one:

The nurse asked, "When is your baby due?".

Yoong Liat, you should give more context!

Thanks, Contrex. I thought it was an indirect question. That's why I left out the question mark.

You describe American English as if it were the only kind, Gargamel. My example is a correct piece of British English. Are you just being provocative?

Punctuation

The traditional convention in American English is for commas and periods to be included inside the quotation marks, even if they are not part of the quoted sentence, while the British style shows clearly whether or not the punctuation is part of the quoted phrase. The American rule is derived from typesetting while the British rule is grammatical (see below for more explanation). As with many such differences, the American rule follows an older British standard. The typesetter's rule was standard in early 19th century Britain; the grammatical rule was advocated by the extremely influential book The King's English, by Fowler and Fowler.

* "Carefree" means "free from care or anxiety." (American style)
* "Carefree" means "free from care or anxiety". (British style)
* "Hello, world," I said. (both styles)

In British style, both single and double quotation marks are possible, but more modern style guides like the BBC's tend to prefer the latter.

The American English rule is often not applied if the presence of the punctuation mark inside the quotation marks will lead to ambiguity, for example in describing commands to be typed into a computer:

In the File name text field, type "HelloWorldApp.java", including the quotation marks.

Before the advent of mechanical type, the order of quotation marks with periods and commas was not given much consideration. The printing press required that the easily damaged smallest pieces of type for the comma and period be protected behind the more robust quotation marks. The US style still adheres to this older tradition in formal writing but usually not in everyday use. Today, most areas of publication conform to one of the two standards above. However, in subjects such as chemistry and software documentation it is conventional to include only the precise quoted text within the quotation marks. This avoids ambiguity with regard to whether a punctuation mark belongs to the quotation:

Enter the URL as "www.wikipedia.org", the name as "Wikipedia", and click "OK".

The URL starts with "www.wikipedia.". This is followed by "org" or "com".

In both styles, question marks and exclamation marks are placed inside or outside quoted material on the basis of logic, but colons and semicolons are always placed outside:

Did he say, "Good morning, Dave"?
No, he said, "Where are you, Dave?"

In the first two sentences above, only one punctuation mark is used at the end of each. Regardless of its placement, only one end mark (?, !, or .) can end a sentence in American English.

References: Chicago Manual of Style, 15th edition; Hart's Rules for Compositors and Readers at the University Press, Oxford.