Some real world modifications would be needed, but it is a very workable design.
The fuel tanks would need to be larger. I would extend them into the area between the two rear landing pods. I don't really see the need for four main engines either, two or maybe even one would work. Converting them from chemicel to nuclear thermal would about double performance.
While the series showed eagles flying through atmospheres and landing on large earthlike planets, real world eagles would be limited to working on the Moon, asteroids, LEO and deep space. Modified unmanned versions could be used as deep space frieghters.