Spark,
So I gather that you scavenged this TX out of the power supply portion of a timer. You can usually assume<G> that they don't put more oomph in the TX than they need. For instance, if your TX leads to 4, 1N4001 diodes, a few hundred microfarads of capacitance and a LM7805/LM340T-5 regulator, sticking up in the air, you can derive a few things. 1.) The 1N4001 is a 1A diode. The TX probably isn't going to be more than 1A, and probably less. 2.) Small caps---> light load. 3.) The regulator, on its best day with a huge heat sink, is working hard at 1.5A. We already know that we aren't drawing 1.5A because they use 1A diodes and small caps. If the transformer is only feeding a 5 volt regulator, it probably isn't more than about an 8 volt TX.
Transformers smaller than your fist are usually 4 amps or less. Many small ones are in the 300mA-450mA range.

So we circuit nerds are going to get a good ballpark hunch on our TX from its size and what we see around it. Then, we might tend to load it down a bit and see how the output drops while keeping tabs on the case temperature. But you MUST put your ohmmeter away if you ever hope to figure out transformers.(unless you think you have an open winding)

Now, all you need is 3 pens and a pocket protector and you're good to go.
Joe