THUS far, congratulations have poured in from a President, a Prime Minister and a First Minister, the Church of England has composed a special prayer, business is hoping for a bump upwards in the economy, and the law of the land will be changed to scrap the centuries-old rules of primogeniture.

All this, and she or he is not even the size of a crown jewel. Baby Windsor, you ain't seen nothing yet.

This time last week commentators were stroking their chins over the Leveson report and what it would mean for the future of the press. This week, one of the biggest tests said media could ask for began with the announcement that a royal baby is on the way.

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And not just any royal baby. This will be the first heir to the British throne born in the internet age. As such, they will forge a unique way in the world when it comes to the media. Whether they want to or not they will be a Columbus, a Drake, an Armstrong, boldly taking the concepts of constraint and good judgment to places they have never been before. The name will be Windsor, but let us be honest, this will be a Truman Show baby. Like the character in the movie, a child who was born on camera and lived on camera, the young prince or princess will not be able to escape the public eye.

Already, the pressures and strains are beginning to show. It was for fear the news would leak on Twitter that the couple announced the pregnancy before the usual 12-week mark. As Kate's acute morning sickness grew worse, they, or more likely their aides, would have known that hospitalisation was likely and, as such, the secret would soon be out. The rush was on to inform family before strangers found out.

The internet buzz had been going on for at least a year. The Duchess, who left hospital yesterday, had only to put a hand anywhere near her stomach for the internet whispers to start. Even the Edinburgh pandas, Tian Tian and Yang Guang, must have shaken their furry heads at the hysteria and thanked their lucky bamboo shoots they weren't royal. (One wonders, indeed, what will happen if the Edinburgh Zoo Two get in the family way soon. Anyone willing to put money on an early independence referendum, complete with posters of Alex Salmond hiding behind something small and friendly that is not Nicola Sturgeon?)

Then there was the prank call in which two DJs from the Australian radio station 2Day, finding the concept of Kate laughing at the carpet just too funny to be ignored, telephoned the King George VII hospital in London at 5.30am UK time, pretending to be the Queen and Prince Charles. In accordance with the usual drill, the call should have been put through to the royal protection squad, who get paid to watch out for rum characters such as Aussie DJs with terrible Brit accents, but instead it was transferred from an unsuspecting receptionist to a hapless nurse.

Trivial as the incident turned out to be – a few red faces, no-one harmed – the 2Day incident, and the rushed announcement to beat Twitter, highlight where problems might arise in future. Furthermore, they show how the Leveson report, in focusing largely on the British press and paying scant attention to the internet and foreign media, was in several crucial respects screamingly irrelevant as soon as it left the printers.

The British media, apart from dispensing enough sugar to rot every tooth from Cumbernauld to Cornwall, has been relatively restrained. Like a naughty child cleaning up its act before Santa arrives, it has been keen to show how grown-up and good it can be. The BBC, for example, aired only a fragment of the 2Day tape, while some newspapers have carried only edited extracts of the conversation between the nurse and the DJs. There was still the same media encampment outside the King George VII, complete with flashbulb light show when anyone of note arrived or left, but this was doorstepping done in the best possible taste.

Is this outbreak of maturity the result of Leveson, or is it the Diana effect asserting itself? Since the princess's death the Palace and Prince William himself once he became old enough have become strict guardians of royal privacy. He is determined that his mother's relationship with parts of the press will not be his. Diana's feelings towards the media could swing from love to loathing and back several times in one week. William, in contrast, is perpetually mistrustful, and willing to take action. Witness his reaction to the publication of photos of Kate sunbathing topless. This is a young man fond of lawyers who write strong letters. His handling of the media is not usually that obvious. Relationships have been formed, sympathisers identified, and strategies laid down. William would make a canny politician.

But will that be enough to save him from the coverage he so clearly fears and despises? He must know the answer to that is probably no, and it won't be the so-called dead tree media to blame. There is a whole worldwide web out there of tweeters, bloggers, chancers and other desperadoes, who see the royal mum-to-be as a fitting object for their juvenile fascination, or a ticket to a big pay day. And if they operate outwith these shores, there is little incentive to play fair or be nice.

What Lord Leveson described as the "ethical vacuum" of the internet is about to become a vacuum cleaner set to blow, spewing out all kinds of rubbish, snatched photos and half-baked notions. And who will police that? Certainly not whatever regulatory body is set up, regardless of whether there is a Leveson law or not. The wild west of the internet will not be tamed so easily.

What the Palace has to trust in is the rather old-fashioned notion that reasonable people will behave decently and proportionately towards others, be they young mothers to be or anyone else.

This is the unspoken law by which most journalism has always operated, the hidden pact between newspapers and their readers, broadcasters and their audiences. It won't always operate perfectly, but left to its own devices it will work well enough.

As for the rest of them, the chancers and the other creepy-crawlies to be found in the web, we shall see. We are all children of the internet age now.