I've created my own app and I want this one to be my launcher. It's a simple app, but it works.
Is it possible to replace the default launcher with my app so that my app always starts by default after booting?
Setting the correct intent filters in your manifest will allow it be prompt you to use it as a replacement:
<activity android:name="Home"
...
android:launchMode="singleInstance"
android:stateNotNeeded="true">
<intent-filter>
<action android:name="android.intent.action.MAIN" />
<category android:name="android.intent.category.HOME"/>
<category android:name="android.intent.category.DEFAULT" />
</intent-filter>
</activity>
See the Intents and Intent Filters documentation from Google.