Yes, the DDA needs amending.
It needs amending for loads of reasons - for one, someone accused of having a dog which falls foul of the Act is considered in law to have to prove their innocence yet almost all other laws require the prosecution to prove the guilt of the accused.
A dog which is merely believed to be a restricted/banned breed may be impounded without proof that he is. He will be taken to a secret location and the owners may not be told where he is much less be able to visit him. He may well - and generally will - stay there for at least a year whilst legal wheels turn.
I have LOADS of reasons for calling for amendments - though I can see argument for disagreeing with yours OP. Because, if your view was to be made law, ALL dogs who bit on private property would be at risk of being killed... including the dog who was protecting his owner against domestic violence or violent burglary.
That doesn't mean that I don't feel for this child but FGS, what were the adults thinking of, allowing a toddler to be that close, with treats, to a dog which isn't even their own and thus well known to them? It beggars belief!
And, as Squeaky said - and she got there first but this was something I wanted to say - please note all you Staffie/Rott/GSD haters/fearers... this was a little Westie, sadly proving what I have always said and often been insulted shouted down about... ANY dog can be a danger when under the control of idiots and it is ALWAYS sensible to ensure that children (or indeed ourselves) aren't allowed to be put in stupid positions.