Because 1848 is not 1859. By then, Russia is thoroughly brassed off with Austria for its refusal to support her in the Crimean War, and Prussia won't help her without getting an equal share in the government of Germany - which Austria, even in this moment of weakness, is still too pig-headed to grant. Since British opinion was sympathetic to the Italians, even if not to the French, effectively Austria was on her own.
In 1848 most of this is still in the future. All anyone can see is that revolutions are breaking out all over the place, while France has just installed another Napoleon as its ruler, so is presumably about to go on the rampage again. With 20/20 hindsight, we know that Napoleon the Little will prove a damp squib, a mere pale shadow of his uncle, but nobody knows that yet. Only 33 years after Waterloo, it's still France that everyone worries about [1], and for Brits at any rate, the next biggest worry is Russia. The Germanic powers are way down the list. Metternich's Austria was disliked in Britain, but not particularly feared, while no one anywhere is the least bit scared of Prussia, which is still seen as the smallest and weakest of the great powers.
And as I've already observed, a "Unified Germany" which includes Austria can only be very loosely unified, since neither of the big boys will surrender control of its army to the other. In practice it can't be much more than a reformed German Confederation, with a somewhat more effective military organisation - which won't scare people until they see it in action, and maybe not even then. Indeed, many are likely to welcome it as a safeguard against revolution and against France.
[1]Incidentally, even in 1859-60 many Brits were still uneasy about France. The 1859 war led to calls for the strengthening of British defences, in case the French turned on us, and France's annexation of Nice and Savoy caused a distinct cooling in Anglo-French relations, in case it proved to be the start of a new round of expansion. In retrospect it all seems a bit hysterical, but that was how people thought at the time.