It is not a good design.
General: Damage Control is a bad idea here. You need to use engineering spaces instead which will give sufficient MSP to keep the ship operational. DCR is not very important for a beam-only ship as the close range of a beam brawl ensures that you won't have time to fix a broken component before you get blown to pieces anyways. Better to use engineering spaces so you can stay operational when, e.g., patrolling a jump point.
On the other hand, an Auxiliary Control would be a good addition here to get more benefit from your officer corps by concentrating them on your limited number of early-game ships.
The armor is probably somewhat excessive, mainly because the protection it offers is not really worth the tonnage that could be used for other purposes (see below).
Propulsion: There is a well-known "3-to-1 Rule" about propulsion design, which is very simply that the space dedicated to fuel should not exceed 1/3 the space dedicated to engines - it can be less, to conserve fuel, but having excess fuel is almost always a waste unless you are building a tanker (and there is no good reason for a multipurpose defense warship to be a tanker). In this case you have 30 HS of engines and 25 HS of fuel - this is purely a waste of fuel, as you could use larger engines with the same total EP (thus, the same cost - no downside here!) and save a lot of fuel due to the better efficiency.
Additionally, 3,128 km/s is very slow for an ion-era ship. The bare minimum for a useful ion drive warship is around 4,000 km/s and even more NPR ion designs will be quicker than this. For a beam-armed ship I'd say anywhere from 4,500 to 5,000 km/s is reasonable. You can achieve this at the cost of some range, or by increasing the overall size of your propulsion section - a pair of size-25 ion engines with 1.2x boost and 865,000 L of fuel will give you 5,000 km/s speed and 26b km range, but requires about 67 HS instead of the 55 you are using now (600 ton difference). There are some good ways to get that tonnage back.
I strongly recommend putting 1000 RP into the Large Fuel Storage as it will save you a lot of BP over using the 1-HS modules.
Weapons: Personally I think turrets for heavy lasers are a waste in most cases. The tonnage that you put into turret tracking speed is tonnage that could be used for more guns (or more engines!) I also agree that more point defense is a good idea, it is a very common newbie mistake to not place enough PD on a ship and then get wrecked by NPR missiles. I'd probably use four non-turret heavy lasers and four 10cm turrets for balanced PD (even better would be 10cm railguns but I understand if RP is a consideration here).
The fire control is overdesigned and under-teched for its purpose, you really do need the range upgrade tech or any beam-armed NPR fleet will have you for breakfast. Even without, I would probably split the BFC into a 4x Speed, 2x Range variant for point defense and a 4x Range 1.7x Speed main weapon variant. This offers redundancy in case of battle damage (important for a ship of decent size).
The reactors are oversized, you produce 10 power and only need 6 (8 if you follow my above rework of the weapons layout). Reduce the reactor size accordingly, though I do still recommend using two reactors for redundancy.
Sensors: The sensor you have is fine, but for a multipurpose warship I think more sensors are needed. At the least size-1 passives are good to make sure that your ship isn't caught unawares, and to allow you to detect other ships without turning on your active sensor(s). If you have the space and RP, a large-resolution active (also size 1) would be good to add also, but you can also have two variants of the class each with a different active sensor resolution (built out of the same shipyard). Once you have the ability to build several classes for your battlefleet, then you can put the passive sensors on specialized ships, but for early-tech multirole ships I think passives are a needed inclusion.
Following these advices, something like the below design is possible. It's not the style of ship I personally would build but I think it is serviceable for the tech level. Note the use of 5x Engineering Spaces instead of a DCR module, which more than doubles the MSP (I've also added a few small maintenance bays to fill tonnage and give enough MSP to repair the engine twice) and gives an acceptable maintenance life. This does come at a small reduction of deployment time and the sacrifice of some armor but I think overall the design is more effective in combat this way.
Off-Topic: Colonial Mk II class Gunship show
Colonial Mk II class Gunship (P) 7,500 tons 233 Crew 837.4 BP TCS 150 TH 750 EM 0
5000 km/s Armour 3-34 Shields 0-0 HTK 48 Sensors 5/6/0/0 DCR 5 PPV 36.8
Maint Life 2.98 Years MSP 393 AFR 90% IFR 1.2% 1YR 66 5YR 991 Max Repair 187.50 MSP
Captain Control Rating 2 BRG AUX
Intended Deployment Time: 6 months Morale Check Required
Ion Drive EP375.00 (2) Power 750.0 Fuel Use 79.81% Signature 375.00 Explosion 12%
Fuel Capacity 870,000 Litres Range 26.2 billion km (60 days at full power)
15.0cm C1 Visible Light Laser (4) Range 80,000km TS: 5,000 km/s Power 6-1 RM 20,000 km ROF 30
Single 10cm C1 Visible Light Laser Turret (4x1) Range 60,000km TS: 12000 km/s Power 3-1 RM 20,000 km ROF 15
Beam Fire Control R80-TS5100 (1) Max Range: 80,000 km TS: 5,100 km/s 88 75 62 50 38 25 12 0 0 0
Beam Fire Control R40-TS12000 (1) Max Range: 40,000 km TS: 12,000 km/s 75 50 25 0 0 0 0 0 0 0
Magnetic Mirror Fusion Reactor R4 (2) Total Power Output 8.1 Exp 5%
Active Search Sensor AS5-R1 (1) GPS 16 Range 5.5m km MCR 497.5k km Resolution 1
Active Search Sensor AS25-R100 (1) GPS 1600 Range 25.7m km Resolution 100
EM Sensor EM1.0-6.0 (1) Sensitivity 6.0 Detect Sig Strength 1000: 19.4m km
Thermal Sensor TH1.0-5.0 (1) Sensitivity 5.0 Detect Sig Strength 1000: 17.7m km
This design is classed as a Military Vessel for maintenance purposes
This design is classed as a c for auto-assignment purposes
Obviously many variations are possible.