Based on your description, most likely the stall current for the motor is in the 1-2 amp range, but it could be higher.
If you want to check it, you have a couple of options, but both involve what is called a "pony brake" - aka, a pair of vice-grips.
Mount the motor such that the body can't turn, then attach a pair of vice-grips to the shaft so that it can't turn. Alternatively, you can don a pair of good leather gloves and grip the shaft; depending on the motor and such, this might be the better method, as you can allow for some slip (indicating near full stall) without burning the motor winding out (which a full stall can easily do).
Hook the motor up to your power supply (note the voltage of the supply with no load) with a shunt resistor in-line; normally you would use a special alloy shunt resistor, but for this simple test, a couple of large ceramic wire-wound 10 watt power resistors, of about 1-5 ohms each, connected in parallel to drop the resistance down, will work fine. Connect a multi-meter set to measure voltage across the resistor. Hook up the motor with the pony brake, note the voltage you see across the resistor. The drop in voltage across the resistor will give you your stall current via application of ohm's law.
Alternatively (but can be worse for your meter if you completely stall the motor out), you can just put the meter on current setting and inline it with the motor, then put the pony brake on it; pick a range greater than 1 amp.
Another way (which I recently found out after picking up my junker power supply) is to use a power supply that has a settable current and current limiting feature; you just hook the motor up, crank the setting to max current, and if it trips, you need a larger power supply. If it doesn't, then check the running current, multiply by 5-6 or so, set the current to that, and see if it trips. Increase/decrease until you get really close. I was doing that to test this power supply with a small motor I had; running current was around 200ma, while stall was around 1 amp (startup current was really close to this, too).
Your transistors are definitely undersized for the task, though - you could try paralleling a few together in your h-bridge, but that would be just an experimental thing; you really want to use larger transistors or mosfets for the job (or a larger h-bridge driver IC). Remember that to get close to the rated capabilities of whatever driver you use, you will need a heatsink.
