Using XSL to move from one node to another

So I want to convert the following using XSL

<doc>
    <data id="priority" level="2" include="true">
        <name>Priority</name>
    </data>
    <data id="cost" level="1" leveltype="number">
        <name>Cost</name>
    </data>
    <data id="date" level="3" include="true">
        <name>Date</name>
    </data>
</doc>

To this

<doc>
    <data id="priority">
        <name>Priority</name>
    </data>
    <data id="cost">
        <name>Cost</name>
    </data>
    <data id="date">
        <name>Date</name>
    </data>

    <!-- ordering matters, though if necessary I can reorder this manually via the DOM instead of XSL -->
    <levels>   
        <level id="cost" include="false" type="number"/>
        <level id="priority" include="true"/>
        <level id="date" include="true"/>
    </level>
</doc>

Basically I want to take the level attributes and make them their own thing. A huge bonus would be if there were some way to remove the level number and use the order of the node instead to represent that.