Strong key generation using PBKDF
There are two inputs to PBKDF2, and key derivation functions in general: the password and a salt. Assuming the attacker knows the salt, all the password hash can do is slow down a brute force or dictionary search (i.e. 1000x the complexity of HMAC with PBKDF2 default iterations), as well as force the attacker to search for each user's password individually. In that case "123456" is an insecure password with any realistic password hash.

If you for some reason could assume that the salt is a strong secret random number of sufficient size, then the keys produced from all of those passwords would be equivalently unknowable. However, in that case you could just use a fast key derivation function. It's not the problem PBKDF2 is meant to solve.

TL;DR: PBKDF2 does not make poor passwords secure, just mediocre ones somewhat less mediocre.