What type of transformer would be required to boost a voltage signal by 2?
Transformers generally fall into two types: power and signal.
Can any type of transformer be used so long as it's frequency response is what you want?
You won't find power transformers operating at 6KHz.

Transformers contain two (or more) coils of wire wrapped around a former. Those coils are inductors and an inductor's impedance increases with frequency. When a former is used, or something to couple the magnetic field of both coils together, iron (or steel) laminated former, ferrite core, then the use of a core will change the relative permeability and can result in a) a stronger magnetic field produced by the inductor, and b) increase in the inductance.  Increasing the inductance reduces the frequency response.

Inductance is a function of the relative magnetic permeability of the material in the core (no core, where there is only air is the lowest value) and is proportional to the cross sectional area of the solenoid.  The bigger the cross sectional area of the solenoid (that is, the greater the diameter), the bigger the inductance will be and the worse its upper frequency response.

Power transformers are typically designed to cope with 50 or 60Hz and designed to handle large currents.

You'd need to think about a pulse transformer which is designed with a much higher frequency response. You could do calculations when you know the inductance of the coils in the transformer or the manufacturer might give you a graph of frequency response.