As you can see, from Dunellen Train Station to Carlton Ave Piscataway is 2.4 miles http://maps.google.com/maps?f=d&hl=en&geocode=&s
about 24 minutes walk if you walk fast.
Taking the Train from Peapack to Piscataway may need to go to Newark Penn Station first as you can see the NJ Transit Map http://www.rususa.com/city/trainmap.asp?region=new+jersey
Carlton Av Piscataway area has Pleasant View Apt, Royal Garden Apt and Princeton Garden Apt that has many IT professionals living there, so if you are also renting there and going to work at Peapack, you may be able to find carpool as alternatives ... http://www.erideshare.com/carpool.php?city=Piscataway
If you do the other way, then carpool may not be feasible as 99% people asking question like this are renting at Piscataway.
I believe there is also NJ Transit bus route along Route 529 from Plainfield to Dunellen to Middlesex Mall as I recalled once I ate at Baja Fresh, this nice amigo told me he renting at Plainfield and took the bus to Middlesex Mall to work, and that route should pass by Carlton Ave. Check with your rental office, they may know.
Pleasantview Apt seems to have active Apartment Rating forum that you may be able to reach people there to find out more direct info ... http://www.apartmentratings.com/rate/NJ-Piscataway-Pleasant-
Ok, I just did a search on NJ Transit site and found this #819 bus probably the closest to you http://www.njtransit.com/pdf/bus/T0819.pdf
and that's the one that amigo told me that he commute from Plainfield to Middlesex Mall, but then, the bus will take you to Plainfield train stn rather than Dunellen Train Stn. The stop seemed to be only 1.6 miles http://maps.google.com/maps?f=d&hl=en&geocode=&s
It seems not easy to use. I would say the best is probably find a carpool from Carlton Ave Piscataway to Dunellen Station, or use taxi. Or if you can find a carpool from Piscataway to Peapack. If driving, it seems to be much easier ... http://maps.google.com/maps?f=d&hl=en&geocode=&s
Do you drive? If you do, you can get a used car at a few thousands, life would be much easier.