The audio signal looks like a great start though you'll get plenty of voltage gain but possibly not enough current gain.
The filiment is suspect, it looks like they are rectifying it and maybe floating it but with such a small unit you could just regulate it at 12v and eliminate a lot of hum.
I tried something similar and built the power too close to the tubes and it caused hum.. I just prototyped a walwart power supply using a 500ma 18vac supply and a cascade rectifier to get 120vdc plate voltage.
I used a 12vdc regulator for the filiment and haven't yet ordered the 120vdc voltage regulator for the plated but the hum was a lot better.
I think my next proto will use a cathode follower and only one stage of gain since mine seemed to not drive the next thing in the pathway very well.