Construct PRF with longer output from existing PRF Assume we have a secure PRF $F$ which takes a key of length $k$, a message of length $l$, and outputs an output of length $o$.
The task it to construct a secure PRF $G$ which takes the same input parameters, but outputs an output of length $2 \cdot o$, by using the first PRF.

My basic intuition would be to construct something like this: 
$$G(k, m) = F(k, m) \| F(k, F(k,m))$$

But there is a dimension issue here, since the length of the output is not the same as the length of the message.

Could anyone give me a hint to push me in the right direction?
The $G$ that you have defined is not a PRF at all. I can distinguish it from random in just two queries. Since I have a feeling that this is homework (correct me if I'm wrong), I'll let you work out how it can be broken.