You probably need to use a mortising bit with a bearing on the bottom (on the shaft end, not the cutter end). These bits come in a variety of sizes and you place the pattern on top of the workpiece. This bit makes a flat bottom cut. It can also be done using a bushing, but you have to allow for the gap between the bushing and bit. Here is an example of a mortising bit.
There are many bits without bearings that can be used to cut a pattern with a bushing, down to 1/8 inch or so, but it doesn't take much to break them.
There are many bits without bearings that can be used to cut a pattern with a bushing, down to 1/8 inch or so, but it doesn't take much to break them.