The brushed Stampede 4x4 has a couple parts that differ from the brushless, most notably the diff gears.
The 4x4 brushed has a 12/47 (3.9:1 ratio) ring & pinion set in the diffs.
The 4x4 VXL has a 13/37 (2.8:1) ring & pinion set in the diffs.
•Traxxas #6755 Aluminum Drive Shaft
•Traxxas #6888X drive shaft adapter
•Traxxas #6879 Front Differential Ring and Pinion Gears
•Traxxas #5379 Rear Differential Ring and Pinion Gears
This gear ratio difference means that a brushless motor swap won't give you the same kind of speed that it will in a VXL Stampede unless you make some changes. You could swap in the VXL diff gears, adjust your pinion/spur ratios, or select a higher KV motor. Personally, I'd keep the diff gears as-is, because I find that the VXL Stampede is over geared and there's not much room to gear down. Having a lower ratio diff gear set will let you run larger pinions on the motor to help dial in your best running temps.
Another issue with going to brushless is that the plastic center driveshaft in the brushed truck probably won't handle the abuse for long. The aluminum shaft from the VXL (TRA6755) can be used along with the adapter part TRA6888X.
Aside from that, you need a motor & ESC. There are a lot of options out there, but my vote for best value goes to a Hobbywing EZRun 60A ESC and a Tacon 3500kv 3650 can. I use this combo in my dad's Ruckus. It's very much equal to the Velineon 3500kv motor in terms of power and speed. With the standard VXL gearing it might suffer the same overheating issues that the Velineon motor does, but geared down in the brushed Stampede, I think it'll be fine.
There's also no shortage of 3660 & larger motors out there, including some very inexpensive ones on ebay. I've used some of those inexpensive motors and I really like them, but to be honest, even that Tacon motor is going to be a lot for an 8 year old to handle. My 8 year old has a 3100kv 3650 can in his Circuit and he can't control it at all. He's been driving that circuit for 4 years, and did great with it right up through the 17 turn brushless I had in it prior, but upgrading him to this 3100kv motor was too much for him. That Tacon in the geared down brushed chassis should be pretty controllable though, especially if you use the punch control and the slipper clutch to help tame the bottom end.