Yes that Beluga would probably get you across the galaxy and back, as long as you don't meet the Big Green Beluga Eater on the way. It will take some time though.
A few general comments:
Sooner or later most explorers feel the need to go somewhere as fast as possible. Fast in ED is different. Each time you jump you spend time fuel scooping and lining up for the next star. With a large enough fuel scoop that time is roughly the same for any ship, and it's longer than the actual jumps. Therefore to travel fast you need to do as few jumps as possible, meaning you want to have as high jump range as possible.
When you build an exploration ship, mass is a concern. Mass eats jumprange and maneuverability. Therefore many explorers tend to go as lightweight as possible. That typically means D-rated modules with lightweight engineering.
You will need some gadgets along the way. A SRV is a must, but I have traveled to some pretty far away places, and I've never needed the AFMUs unless you use neutron stars to boost the FSD.
When you fuel scoop the ship gets hot. One way to deal with that is to engineer the Power Plant to get a lower efficiency. This is weird, since normally high efficiency is good. Not so in ED. If your PP has lower efficiency, it produces less heat. With a normal A-rated PP the efficiency is 0.40. Not bad, but with a Low Emission engineering + Thermal Spread you can go as low as 0.13, basically "meaning" one third the trouble with heat. It's much more complicated that that
Once you get tired of jumping from star to star, the Beluga is almost as large as a Fleet Carrier, so like the SRV, I like to bring a Ship Launched Fighter on my exploration Conda. It's like that ATV on a large Mobile Home. I see you also have thought about that.
You won't need a large shield. However, I do like proper thrusters on my exploration ships. It keeps you safe at high G planets, and it makes the ships more fun to fly. That also means that you should look at the Power Distributor. Too long boost intervals is a killer of fun.
My favorite exploration ship is much smaller and less luxurious than the Beluga, but there might be stuff you can use.
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