There are two paths to Downtown Disney from SSR--and T-Rex is fairly close to "in the middle"--it may be a tiny bit further taking the path that puts you into Downtown Disney on the West Side, right near Cirque and DisneyQuest--but not much.
It's that path (the West Side path) that's closest to Springs...the easiest way to find it is to head to the boat dock "behind" the Carriage House...you'll see a wooden bridge on your right...follow the path across the bridge and bear to your left...fairly soon you'll see a big parking lot, w/Cirque on the far side...you can follow the sidewalk, or cut thru the parking lot (I've never seen it even close to full)...cutting thru the parking lot cuts off maybe 2 minutes worth of the walk...then, of course, you just take a left in West Side and go past all the West side shops/venues, over the bridge into Pleasure Island, thru Pleasure Island, and on to T Rex, which is fairly close to the "far side" of Pleasure Island/Marketplace "merge."
The other path parallels the canal...you pick it up "behind" the pool at Congress Park (actually, you can pick it up a bit closer to Springs behind the first of the Congress Park buildings, but that's harder to describe)...follow the walkway next to the canal to its end, which will put you on a road (forget its name)...turn right and you'll see the Marketplace bus stop straight ahead (very close)...when you get to the bus stop, make an immediate right to go into Marketplace and follow the Marketplace paths to T Rex (towards Pleasure Island)...
From Congress Park to the Marketplace bus stop (starting at the Congress Park pool) is no more than 10 minutes, at a pleasant "strolling" pace...it's another 5-8 minutes, depending on how fast you walk, from Springs to Congress Park...The West Side path shouldn't take you longer than 10 minutes from the boat dock to the Cirque parking lot...it's maybe 5 minutes from Springs (depending on which building you start from) to the path by the boat dock...
As I recall, the entire distance from the beginning of Marketplace to Cirque (the end of West Side) is close to but less than a mile...so to T Rex would be between 1/3 and 1/2 a mile from the Marketplace bus stop, and maybe 1/2 mile or so from Cirque...
Very pleasant walking!
Hope this helps!