The design will work and have no immediate problem but a few remarks is in order...
The range of the ship is way too long for what you want such a ship to perform. You also want such a ship to be as fast as possible so you should design an engine with a higher power efficiency. Speed is paramount for such a ship, both for offence and defence.
You also have a repair capacity that is awfully low in comparison with what you need. There is a great risk that a squadron of these ships will loose one due to maintenance problem if you go to the system next door.
I would personally reduce the deployment time to 0.5 month to reduce the crew needed and increase the engineering so you have at least 1 year of maintenance life. Make a more powerful engine, give the ship less fuel and add at least one maximum spinal mounted laser in addition to the two 30cm lasers that you have.
The ship has no protection against missiles and both ASM and AMM will be a huge problem if the enemy use these. I would perhaps either design an escort ship with the same engine carrying gauss cannons (or lases cannons if your research is too poor on gauss technology) or make the ship slightly bigger and include a twin turret gauss defence system.
Remove the search sensor for a smaller resolution "1" sensor, you only need long enough range to engage your enemy and missiles. You must rely on some dedicated scout ship to actually locate the enemy, these are too expensive to use for that.
Those are my main concern about the design.
Oh... and... you can't call the ship "Lazer Frigate Mk1 class Cruiser", it can't be a frigate and a cruiser at the same time... unless you mean that a frigate is a cruise ship such as the old frigates of the past.
