A larger NCX (or Overdrive/Gator) in 9.0 m2 or an Element 9.5 m2 will work pretty nicely on your '05 Carve 145.
The limiting factor to earlier planing may not be sail size.
If you are wanting to plane as early as your friend on the FE board, or as early as any other local sailors on Formula; FE; or Apollo boards, you will most likely be a bit disappointed in your Carve 145 with the 9.0-9.5 m2 rig.
You will drop the planing threshold a little with a larger rig, for sure, but you simply cannot drop it down to be competitiive with the wider boards mentioned above.
Beyond 8.5 m2 I'm pretty sure the "gain" from a larger rig drops off quicly unless you have the wide tail and big fin found on the Formula/FE/Apollp boards.
This is not meant to discourage you at all.
The bigger sails will work (up to 9.5 m2 for sure) but the larger sail; longer mast; longer
carbon boom will be pricey and only you can decide if the cost/benefit ratio is acceptable.
Hope this helps,