Should we be worrying about quantum computers or is it possible that at that time a counter technology can also be developed?
Short answer: No.
Slightly longer answer:
Definitely not in the foreseeable future. Quantum computers are not magic machines.
It will still take lots of years until usable QCs will be built.
And if they are finally in a stable state with the ability to program them properly, one would still need to develop an efficient algorithm.
It is not like you would give it the public key and say 'crack it' - and 10 minutes later you have the private key.
Even IF this was the case (which would still take lots of years to reach this state), simple stopping of address-reusing would circumvent it. THEN we would basically be at the same level of security as IOTA.
But instead of stopping address reuse, we can simply fork into a better (quantum proof) algorithm. We will have more than enough time for this.
Now, if we are also talking about attacking hashing algorithms in addition to the elliptic curve (where it wouldn't be enough to stop address-reuse), the world would have far more problems than just BTC's security.
Anything else would also be at risk (TLS, banking, encryption, etc..).
However, in this case BTC can still simply fork to a new algorithm.
So.. in the end.. No, quantum computer will note harm BTC at all.
And if you here someone else talking garbage that QCs will break BTC in no time - they don't have a clue at all regarding what they are talking about.
Even with existing, fully functional QC's it probably still would take years to create an efficient algorithm to be able to crack private keys.