http://www.faa.gov/airports_airtraffic/air_traffic/publications/atpubs/aim/Chap4/aim0403.html
AIM 4-3-2 describes segments of the traffic pattern, and the departure leg of the traffic pattern as follows:
Departure leg. The flight path which begins after takeoff and continues straight ahead along the extended runway centerline. The departure climb continues until reaching a point at least 1/2 mile beyond the departure end of the runway and within 300 feet of the traffic pattern altitude.
However, the above paragraph does not describe a right-hand exit from a left traffic pattern. The recommended entry, operation in, and exit of a traffic pattern is found in AIM 4-3-3, with diagrams, and is described as follows:
Key to traffic pattern operations
1. Enter pattern in level flight, abeam the midpoint of the runway, at pattern altitude. (1,000' AGL is recommended pattern altitude unless established otherwise. . .)
2. Maintain pattern altitude until abeam approach end of the landing runway on downwind leg.
3. Complete turn to final at least 1/4 mile from the runway.
4. Continue straight ahead until beyond departure end of runway.
5. If remaining in the traffic pattern, commence turn to crosswind leg beyond the departure end of the runway within 300 feet of pattern altitude.
6. If departing the traffic pattern, continue straight out, or exit with a 45 degree turn (to the left when in a left-hand traffic pattern; to the right when in a right-hand traffic pattern) beyond the departure end of the runway, after reaching pattern altitude.
Note that two pattern departures are described: the straight-out deprature, or a 45 degree exit left, in a left hand pattern. From a regulatory perspective, there is no requirement to execute either one, and we all know that crosswind and downwind departures are common at most uncontrolled fields.
The only regulatory requirement for traffic pattern observance comes from 14 CFR Part 91.126, and this stipulate that one must make turns to the left unless otherwise specified, as follows:
§ 91.126 Operating on or in the vicinity of an airport in Class G airspace.
(a) General. Unless otherwise authorized or required, each person operating an aircraft on or in the vicinity of an airport in a Class G airspace area must comply with the requirements of this section.
(b) Direction of turns. When approaching to land at an airport without an operating control tower in Class G airspace—
(1) Each pilot of an airplane must make all turns of that airplane to the left unless the airport displays approved light signals or visual markings indicating that turns should be made to the right, in which case the pilot must make all turns to the right; and
The regulation here could be worded just a little better, particularly 91.126(a), which states "on or in the vicinity of an airport." This suggests by construction of language that the regulation applies not only to the airport traffic pattern, but to aircraft on the airport (as opposed to over it)...and we know very well that making only left hand turns while on the surface is not only an extreme inconvenience but in many cases a physical impossibility.
What the regulation does not do is address traffic pattern departures. It simply provides a blanket coverage for operations "in the vicinity of" the airport. "Vicinity" isn't defined in Part 91, or in Part 1. This does suggest that one should leave the vicinity of the airport before executing a turn contrary to the traffic pattern, however. Where left traffic is in play for the runway in use, then one should not be in the vicinity of the airfield if one intends to make a right departure.
From a practical point of view, if one elects to make a right turn on the departure leg, while 300' below the traffic pattern, this places one turning directly into traffic which might be entering the pattern on crosswind leg, or turning from an upwind to a crosswind leg...and climbing directly into that traffic's path. Additionally, if other traffic is approaching the opposing runway (you're departing runway 13, and other traffic is flying a pattern for 31, for example), you're turning into that traffic's pattern.
A good, conservative answer is that per the AIM and the regulation, if you intend to perform a right hand turn, it shouldn't be done below the traffic pattern altitude, and shouldn't be done until one has flown out beyond the vicinity of the airport (eg, left the traffic pattern).
