With dimming you have all kinds of potential issues. But without dimming, all you should need to do is match:
- Voltage (many light fixtures can take a wide range of voltages, some have a very narrow range)
- Current (the total of all the light fixtures has to be <= the maximum output of the transformer or circuit source)
- AC vs. DC
Typically lights will be high voltage (e.g., 120V or 240V) or low voltage (e.g., 12V or 24V). But with LEDs things get a bit tricky. Because LEDs don't run on AC (technically if the voltage is right, you could run an LED directly from AC, but it would only make proper use of incoming power in half of each cycle), they have drivers which convert the incoming power to a proper low voltage and DC. A traditional transformer changes the voltage but keeps it AC.
So you really have two practical options. The third, impractical option, is to use 120V or 240V LEDs (which are really LEDs with drivers to convert 120V/240V AC to low voltage DC), but that would mean bringing 120V or 240V power into your landscaping, which is potentially very dangerous. Low voltage wiring has very few rules because it is relatively safe. It is quite likely that the existing wiring would not meet code for use with 120V power.
Existing Transformer - Keep the existing transformer and find matching LEDs - i.e., MR11 base, compatible with 12V AC power. Don't worry about current - the LEDs will use less than the halogens and that should not cause any problems.
New Transformer or Power Pack - Replace the existing transformer with a new transformer (but a different voltage matching the LEDs you find) or a power pack ("wall wart") to convert from 120V or 240V AC to low voltage DC, to match new LEDs that are compatible with the specific DC voltage. If those LEDs use an MR11 base, great. If not, you will need to replace the bases to match the LEDs, or hardwire the LEDs. Keep in mind that good quality LEDs should last significantly longer than halogen bulbs, so replacement should be in the range of several years rather than several months.