That design lacks any fuel.
Well, to put it in a nutshell:
Don't build fighters until you got the tech to back it up.
Get an additional Engine level, the jumps are faster early on and your fighter would be obsolete within a year. (I would personally wait for Ion)
Get atleast the first 2 levels of fuel efficiency, they are cheap, and it pays off.
Theres Miniaturization tech;
A command module will hold 20 crew for just 0.1 size.
Fighter Engineering spaces are equally small, and can keep a fighter running for years without maintenance.
A small fuel tank, holding 10k liters, will be sufficient for combat fighters, and saves some space.
And always keep in mind that a Bridge is not needed for Ships below 1000 tons.
Also, Beam fighters are more difficult, their weapons tend to be rather heavy, making them slower, while their range puts them in danger.
Go for Mesons or Reduced Size Gauss cannons, though Lasers become interesting when your able to reduce their size and still have a 5 second fire rate.
If you have some reasonable tech in that respect, try to go Missiles first, you'll be able to fire them from outside the enemies Beam range.