The level of the stream may change season to season so the means to pump water from a higher or lower head and flow rate is an issue. While there are many good solutions, mayhap simplicity is the issue at hand. While not efficient, a simple paddle wheel driving a small piston pump that intakes water through a flapper style valve would be sufficient. By paddle-wheel I mean a number of convex paddles attached to the end of a hub, with the hub attached to a short axle that operates like a windshield wiper motor (or bicycle peddle being driven by it's chain). Then the off-set is used to drive a small flapper-valve pump. Small! Your not after quantity with something like this, but constant operation instead.
For reference, we did this in Tennessee when I was a kid (76-81) useing wood and sheet-metal to get water closer to a new tobacco patch, raising water 16 feet from the level of the creek before sending it along the way in a 1/2 pipe.
Made of sufficiently light materials a paddle wheel will operate in shallow water. The pump; driven by the paddle wheel would have to be quite small to ensure operation in a low flow situation, but usually constant flow from a source is preferred to intermitant operation. I would start with a paddle about 12 inches by 12 inches in a stream such as you describe. Attach the paddles to a series of spokes around the driven axle. 8 to 12 paddles seemed to be the number we used on the farm.
If your pump stalls the paddle-wheel and you can't get anymore water on the paddles, then you need to start again with a smaller pump.
The simple pump I am referring to is a couple pieces of pvc, one sliding inside another. The inner piece would have a flapper valve at the base to cycle water inside when it is drawn back by the paddle-wheel. Then as it is pushed in the other direction the flapper closes and the water is pushed along the pipe. The two pieces do need to be a loose fit and should move freely making a little sanding necessary on the inner pvc pipe a times. It functions the same as an old fashioned bicycle pump. The entire pumping affair is submerged.
As the idea is to get water up and over the hump so to speak, I would pump up to a "slew" that feeds something small. A typical garden hose in size would be good for testing and using a slew (box) would allow for a place to filter and remove debris before it gets a chance to clog up the works. The shorter the distance to the slew, the better.
Alternate pump - While I doubt the type pump that is driven by a drill (available at Lowes, Home Depot, etc) would work efficiently driven by the paddle wheel such as I am speaking of, it may work reasonably well if it were completely submerged.
If I have made this terribly complex please let me know and I will try to draw it out. Good luck.
GeorgeT