No, you have 2x512MB RAM modules so only 1GB total.
You can put up to 4GB in that machine, if you want to replace those with 2x2GB modules
You could do it for about $60 although you do not have to buy from OWC. You can take those RAM specifications and shop for RAM from crucial.com or somewhere else.
While 2GB is the minimum for Mavericks, you'd find the whole 10.9 experience much nicer if you went for the 4GB upgrade.
P.S. what you have does appear to be the default setup for a mid-2007 model Mac mini - http://support.apple.com/kb/SP7
No.You need to install more memeory. See the following:
Also, you may actually have a 2007 Mini since Apple did not make a 2008 Mini. A 2007 can only go to 10.5
A 2007 is MB138*/A, MB139*/A, Macmin2.1
A 2009 is MB463*/A, MB464*/A, Macmin3.1
Your Mini can only go to OSX 10,7. I know because your initial post's screen shot shows a 1.83 GHz processor, 2009 one, which can go to Mavericks have either a 2 or 2.26 GHz processor.
OS X Lion system requirements
To use Lion, make sure your computer has the following: