Yes, there is something you're missing. If you're familiar with special relativity you know that velocities don't add the same simple way they do in Newtonian mechanics. If one spaceship is moving at $c/2$ to the right and another is moving $c/2$ to the left, the relative velocity between them is not $c$, as one might expect, but $4c/5$.
In general relativity the same kind of thing applies to distances as well as velocities. In flat space we define the distance between two objects as the length of the (unique) straight line from one to the other, but in general relativity space can be curved and there is no such thing as a "straight line". The closest analog is a geodesic, which is a smoothly curved path between two points whose length is a (local) minimum. The distance to the quasar you quoted is defined as the length of a certain geodesic connecting it to us.
But there's no reason to expect geodesic distances to behave just like straight-line distances in flat space. In the FLRW metric (which defines the basic shape of the whole Universe in big bang cosmology), there exist geodesics that are longer than the geodesic from the big bang to us used to define the "age of the universe". So having a quasar whose "proper distance" or "comoving distance" from us is 29 billion light years is not a contradiction at all.
BTW, another seemingly contradictory thing you might run into is relative velocities faster than the speed of light. This can happen because relative velocity is also a tricky thing in GR, which is only defined once you decide on a specific path to "parallel transport" the velocity vector along. The relative velocity between two nearby objects is well-defined and can never be greater than $c$, but the relative velocity between two very distant objects (defined a certain way) can be greater than $c$.