The L35 Ghost is a good putter, but my advice is to wait - you are putting fine at this stage. If anything, a new wedge but the longer you wait, the better the clubs (including wedges).
Good wedges will get you closer and improve the scrambling, thus making putting easier from closer distance.
Before upgrading, are you a ding or off-ding putter? As a ding putter (well hmmm, I try to be!) the Nike Method is excellent and this is the putter I would recommend. The real advantage for me was the scale and allowed for easier calculations.
The negative is putts under 10 feet need extra oomph as it is "soft" under this distance.
In summation....wait and try and earn as many free credits as you can, as the higher the tier, the better the equipment you will require (to score well anyway).
Just have fun and learn the game until then.