If I remember correctly, according to Antonia Fraser, Catherine Howard did conceive early on during her marriage to the king, but suffered a miscarriage very soon after (c. 1540). And just a minor nitpick: the boy would probably have been christened "Henry", given all of the those sons of King Henry VIII who lived long enough to be baptized were either named "Henry" or "Edward".
Assuming Catherine Howard conceives early in her marriage, this change of events could butterfly away the entire Thomas Culpeper affair (assuming it took place). Remember, before anything was known of her activities with Culpeper, the main complaint against Catherine was her earlier sordid private life at the house of the Dowager Duchess of Norfolk, before her marriage. If anything, her giving the king a healthy son will ensure that this is hushed up.
Now, Catherine Howard giving the king a son will change a lot of things, even if she dies in childbirth. First, it means that the power of her uncle, the 3rd Duke of Norfolk, and the rest of the Howard family is cemented at court (since the family's downfall was largely the result of the queen's own fall and execution). This also means that the more conservative religious faction at court stays in power, such as Bishop Gardiner and the rest.
This is going to largely affect the reign of King Edward VI and the English Reformation. Remember, according to the terms of King Henry VIII's will in OTL, the regency was left to a council of sixteen members. The Duke of Somerset (at this time Earl of Hertford) was only one of the members of the council, though he did manage to seize power in a coup of his own within a few weeks of the king's death. ITTL, this is going to be very difficult. Without a doubt, the Duke of Norfolk will be on that council, along with Bishop Gardiner and other reactionaries--indeed, Dudley might not even be appointed to the regency council ITTL, and we may see his influence butterflied away. We might also see Norfolk seize power, probably more in a John Dudley like fashion of gaining control of the council and ruling as de facto regent through the body.
Also, a large amount of King Edward VI's education was supervised and arranged by Queen Catherine Parr in OTL. Without her marriage to the king, King Edward might just be a very different sort of person. Indeed, he'll probably have far less radical protestant leanings, considering that he'll grow up in a time when the Reformers are very weak. Regardless, if Edward VI dies young as in OTL (not necessarily a sure thing, since he wasn't as sickly as many have later claimed until his early teens), then you will see his half-brother come to the throne as King Henry IX.
King Henry IX will largely be under the influence of his great-uncle Norfolk in this scenario and the rest of the Howard faction. He'll probably be a religious reactionary as well, though I can't see him being a Catholic per se (after all, nobody, save for perhaps Mary and Pole, wanted to really give the monasteries back their land). Queen Catherine (if she is still living) may have some role in the regency, probably de jure only, though this isn't exactly a sure thing, considering that there isn't a great deal of precedent for the queen dowager having a role in her son's regency, or even upbringing.
This all means that the Henrician Church settlement stays mainly intact and the Howards remain very powerful, at least for a time. England will also keep Calais for longer than OTL, and there may be more push for a Anglo-Spanish alliance than an Anglo-French one (the latter of which was largely motivated by Dudley and the failures of Somerset in northern France).
Also, consider one thing: this "King Henry IX" is about the same age as Queen Mary of Scots. WI King Henry VIII tries to get her betrothed to his younger son, instead? The Scots may be more willing to buy this (win-win, after all, since King Henry puts his younger son on the Scottish throne and the Scots don't lose their independence), which means no Rough Wooing--something that will ease English financial burdens in the coming years. Queen Mary might just stay in Scotland, which makes things very easy for her to wed her cousin King Henry IX and possibly unite the two crowns.