Your answer is yes you are early but that depends on the weather. Your pepper plant could dye from a frost but the chance of frost is low. Look here http://ucanr.org/sites/gardenweb/files/29030.pdf
Here is more information :
Don't be in a rush to transplant outside. Cold temperatures can weaken plants and they may never fully recover. A few days at 60 F to 65 F with reduced water will help harden plants and reduce transplant shock. Over-hardened plants grow slowly after transplanting.
Set plants out 2 to 3 weeks after average last frost when the soil has warmed and the weather has settled. Plant them 12 to 24 inches apart, in rows 24 to 36 inches apart, or spaced about 14 to 16 inches apart in raised beds.
Use black plastic and/or row covers to speed soil warming and early growth. Use caution with row covers not to overheat plants and cause them to drop their blossoms.
If not using black plastic, mulch plants after they are well established and the soil has warmed to retain moisture and control weeds.
Peppers can be temperamental when it comes to setting fruit if temperatures are too hot or too cool. Night time temperatures below 60 F or above 75 F can reduce fruit set.
You can see the reasons for waiting until late March in your area but you can use black plastic mulch and a clear plastic row cover to plant early and that is our recommendation and thank you for using ask an expert