The transition from Republic to Empire was not merely cosmetic
The Emperor did plan to eventually disband the Senate, but it was politically expedient for him to keep it for the time being. Moreover, the Senate was so servile that it did not hinder Palpatine in any meaningful way:
“The Senate is supportive?”
“Now that it serves rather than advises.” The Emperor swiveled slightly in Tarkin’s direction. “Better to surround oneself with fresh loyal allies than treacherous old ones.”
“But do you even need them, my lord?” Tarkin asked in a careful, controlled voice.
“The Senate?” The Emperor could not restrain a faint smile. “Yes, for the time being.”
canon novel Tarkin, p. 76
Also, Palpatine did restructure the government when he announced the Empire: he established sector governors (Moffs) in the Sector Governance Decree.1 We currently don't have a good canon source for the powers of the Imperial Senate, but presumably the Imperial Senate lost some of its power since it now had to compete with the Moffs for control of local systems. This is supported by the following statement from Tarkin:
The Imperial Senate will no longer be of any concern to us. I've just received word that the Emperor has dissolved the council permanently. The last remnants of the Old Republic have been swept away...The regional governors now have direct control over territories. Fear will keep the local systems in line. Fear of this battle station.
Star Wars: Episode IV A New Hope
Palpatine waited to disband the Imperial Senate until
- The Death Star was completed, so that it could be used to instill fear in local systems.
- An Imperial Senator (Princess Leia) was caught aiding the Rebel Alliance.
Since Palpatine planned to eventually disband the Senate, he also needed to restructure the Republic as an Empire -- a republic without a legislative body like a senate is a contradiction in terms, but it is possible for an empire to include a senate.
So why didn't Palpatine also wait to announce the Galactic Empire?
Palpatine could have waited until he was ready to dissolve the Imperial Senate before announcing the Empire. After all, he had acquired a number of emergency powers as Supreme Chancellor which effectively made him a dictator. The reason he announced the Galactic Empire when he did is that he was striking while the iron was hot, so to speak. The Clone Wars were like a Reichstag fire on steroids2: they were used by Palpatine to prove that the Republic was ineffective and that stronger, centralized leadership was required (that's how the Republic won the war, at least in public appearance). This is how Palpatine justified the creation of the Empire:
In order to ensure our security and continuing stability, the Republic will be reorganized into the first Galactic Empire, for a safe and secure society which I assure you will last for ten thousand years.
Star Wars: Episode III Revenge of the Sith
This justification was the culmination of Palpatine's entire political life up to this point, in which he continually undermined the Republic's form of government. He started with the invasion of Naboo by the Trade Federation:
...the Republic is not what it once was. The Senate is full of
greedy, squabbling delegates who are only looking out for themselves and
their home systems. There is no interest in the common good...no civility,
only politics...its disgusting. I must be frank, Your Majesty, there is
little chance the Senate will act on the invasion...the Chancellor has little real
power...The bureaucrats are in charge now...Our best choice would be to push for the election of a stronger Supreme Chancellor. One who will take control of the bureaucrats, enforce
the laws, and give us justice.
Star Wars: Episode I The Phantom Menace, Palpatine advising Queen Amidala
Later, he showed that the Senate proved inept by initially opposing the Military Creation Act while the Separatists were poised to attack with a massive droid army. If the clone army hadn't already existed, the Republic would have had no defense against the Separatists.
Thus Palpatine announced the creation of the Empire at the perfect time: the Clone Wars had just ended and the Jedi had just been discredited, so a war-weary Senate and populace -- with the failures of the Republic system of governance fresh in their minds -- approved of the change with "thunderous applause". Conversely, if Palpatine had waited until he was ready to disband the Senate decades later, it would have made no sense to the populace to suddenly change the entire system of government from Republic to Empire.
1 Wookieepedia cites the Revenge of the Sith novelization for this decree.
2 The analogy is especially apt here, as Palpatine's comment that the Galatic Empire would last for "ten thousand years" echoes the Nazis' claim that the Third Reich would last a thousand years. Wookieepedia suggests that this historical parallel was deliberate on the part of George Lucas.