Until the widget is updated, here are a series of steps to get a Google+ button on your WordPress site, based on my experience and the information already provided in the readme.txt of the widget.
1) Download a set of Google+ icons
There are a number of different icon sets out there. Here's a link to the set I chose, which features "g+" and regular "+" icons in all standard sizes: "http://www.seriftuts.com/wp-content/uploads/2011/07/google_plus_icons.zip" This particular set is free for use, without attribution. You may want to rename the particular icons you want to keep them straight. For instance I renamed "32x32.png" to "googleplusicon.png".
2) Upload the icons you need onto your site
As per the readme.txt included in the Social Media Widget, you need to upload the icons into a web-accessible directory. Do NOT put them in the Social Media Widget directory, as you will then lose them when the widget is uploaded. What I did is FTP to my site, and created an "icons" folder under "wp-content".
3) Figure out the URL of the icon you want
Once you've done the upload, you can figure out the full path URL to the icon. For me, it ended up being: "http://blogname.com/wp-content/icon/googleplusicon.png"
4) Figure out your Google+ id
For some reason Google has only provided your profile as a long string of numbers. To figure out what your id is, go to your Google+ profile and look for the string of numbers in the URL bar. Mine, for example, is "102754391066567417046". My profile URL is therefore "http://plus.google.com/02754391066567417046".
5) (OPTIONAL) Make a nicer looking Google+ profile URL
If you want to make an easier to remember URL for your Google+ profile, there are a number of services. I used "http://gplus.to" On their site you can enter your profile ID (the string of numbers) and a nickname that you want - they'll then give you a nicer looking URL that redirects. So for example mine is now "http://gplus.to/cgully"
6) Bring it all together!
Now you have your icon, and your Google+ profile URL. Go to the Social Media Widget in your WordPress Dashboard. Look for "Custom Services". For "Custom Service Name" write "Google+"; for "Custom Service Icon URL" enter the URL you figured out in STEP 3; for "Custom Service Profile URL" enter your Google+ Profile URL as in STEP 4 OR STEP 5.
That's it, that's all. If you have any questions about this particular method, I'll try my best to help.