In light of the accepted answer I still believe there is a misunderstanding of this situation, so I'm going to add a little more clarification.
First and foremost - Dumbledore had no problem with the Reasonable Restriction of Underage Sorcery. In fact throughout the books there's no indication that any adult, in any faction, has a problem with it - it's simply a law that stops (discourages, really) young kids using magic before they are trained. This is viewed by all as a...well, reasonable thing. And it is!
Specifically what Dumbledore is afraid of (the "this" in "this was exactly what Dumbledore was afraid of –") is that the Ministry, knowing they can use this law as an excuse to bring Harry in, would set him up in some way so as to force him to break it. She's saying "this" because it worked, and they are in the exact situation Dumbledore feared they would engineer.
She's not referring to the law, she's referring to the incident that caused Harry to use magic outside of school.
Context is important here - she says this directly after Harry is attacked by the Dementors in Little Whinging and he is forced to defend himself by using magic. Dumbledore is well aware that the Ministry is corrupt and seeking to discredit Harry in any way they can. He has stationed guards (Mundungus and Mrs Figg) to watch Harry, and this is exactly this sort of thing he told them to watch for - an unexpected incident that would cause Harry to break the law, allowing him to be pulled up by the Ministry and expelled/imprisoned.
"I’ll take you to the door," said Mrs. Figg, as they turned into Privet Drive. "Just in case there are
more of them around... oh my word, what a catastrophe... and you had to fight them off
yourself... and Dumbledore said we were to keep you from doing magic at all costs... well, it’s
no good crying over spilt potion, I suppose... but the cat’s among the pixies now."
And of course it is later revealed that Dumbledore was correct - Umbridge sent the Dementors for exactly this reason.
"What Cornelius doesn’t know won’t hurt him," said Umbridge, who was now panting slightly as she pointed her wand at different parts of Harry’s body in turn, apparently trying to decide where it would hurt most. "He never knew I ordered Dementors to go after Potter last summer, but he was delighted to be given the chance to expel him, all the same."
"It was you!" gasped Harry. "You sent the Dementors after me?"
"Somebody had to act," breathed Umbridge, as her wand came to rest pointing directly at Harrys
forehead. "They were all bleating about silencing you somehow - discrediting you - but I was the one who actually did something about it... only you wriggled out of that one, didn’t you, Potter?"