You will need to be very comfortable with Green functions and complex integration. Also, a solid quantum foundation in the harmonic oscillator and dirac notation. It can be done without a solid background in quantum...but to a certain extent your understanding will be superficial...i.e you could probably perform the calculations, but the context will be muddled.
I'm not too fond of peskin personally. I think if you used 'Mandl and Shaw' ,'Schrednecki' and Ryder to compliment Peskin then you might be ok. Also, Griffiths Intro to particle physics has a nice introductory section into QFT somewhere around chptr 11 I think. Introduces the QFT lagrangian for a scalar field and the Euler lagrange eqtns.