hey.. what a interesting topic (for me)
iam currently trying to build also an push-trailer..
first: i have bought this one:
here a pictures:

bought it for 45 Euro
(there are a lot of this trailers at ebay)
its rated: 6kg empty weight
35kg payload possible
16" wheel
there are also very similar, but better quality trailers (but of course also a lot more money)
for example BOB-YAK:
http://www.bikesandtrailers.com/bike..._2005_zoom.jpg
or the BOB-IBEX with suspension !
http://www.pedalkraft.de/_borders/ibex.jpg
so..
iam in the moment waiting that i get the trailer..
i hope that it will be possible to use parts (you can order single parts of the kit) of this kit to motorize the trailer:

but i want to use not the original Motor with the (i think not so quiet) planetary-gear
the unit has a free-spinning-unit, so no drag when driving without motorpower
i want to build my own motor for it...
(brushless outrunner, weight: about 300g light, ~300rpm/Volt
--> with 15V that would be around 4500rpm at the motor
with the 1:10 gearing of the chain i would not need any planetarygear
-> the wheel would spin with 450rpm -> ~500m per minute -> 30km/h topspeed -> benefit of the small 16" wheel (don´t need that high gearing)
for a gimick: i want it to be able to switch between triangle and star-configuration.. example:
20km/h with Star for hills -> 35km/h for flat when using in triangle-configuration
however:
for the above shown kit i need rims with 36 spokes !
have heard, that there are 16" wheels availabe with 36 spokes
without any payload i think the whole unit will be ~10kg including the batts..
question is: how much traction will the trailer have with only that few weight (some of the weight is even not carried by the 16" wheel but by the rear-wheel of the bike...)
i mean: on a steep hill, this 10kg trailer (with less than 10kg load on the 16"-wheel) will maybe loose traction and not be of great help.. we will see...
if it works out to be good, maybe i will invest in one of these (which looks much cooler):
Extrawheel – Fahrradanhänger :: Einradanhänger :: Anhänger

26" or 28" wheel... this with an hub-motor might be cool..
here a very nice Picture of it:
http://www.bobtec.de/img/Extrawheel-...r_FN-Trike.jpg
for more pictures of different electric push-trailers look here:
BobYak Fahrradanhänger mit Elektromotor
also nice and motorisable:
Oxtail Fahrradanhänger - Der Anhänger
(look in the gallery)
and more price:
Weber Products Online. Fahrradanhänger | Kupplungen | Zubehör
there are already 2 pics of a motoriszed version:
more detailed picture of the drive unit:
http://www.bobtec.de/img/monoporter-detail.jpg