In Android Webview, am I able to modify a webpage’s DOM?

To expand on CommonsWare’s correct answer:

WebView webview = new WebView();
webview.setWebViewClient(new WebClient());
webView.getSettings().setJavaScriptEnabled(true);
webview.loadUrl("stackoverflow.com");

then in WebClient:

public class WebClient extends WebViewClient {
    @Override
    public boolean shouldOverrideUrlLoading(WebView view, String url) {
        view.loadUrl(url);
        return true;
    }

    @Override
    public void onPageFinished(WebView view, String url) 
    {       
        // Obvious next step is: document.forms[0].submit()
        view.loadUrl("javascript:document.forms[0].q.value="[android]"");       
    }
}

In a nutshell, you wait for the page to load. Then you loadUrl(“javascript:[your javascript here]”).