Tom,
I consulted "The Pennsy Era on Long Island" by Ron Ziel. There are several photos of H-3s but none in which there is a caboose. LIRR #163 was built by Baldwin in 1892, sold to the LIRR in 1903, and retired in 1924. Ziel states that in 1916 the LIRR H-3s were downgraded to switching duties when the PRR sold 15 H-6s engines to the LIRR.
I also checked "Pennsy Power" by Alvin Staufer. It had one builder's photo of an H-3a but no information about cabooses.
The best information I could find was in "Cabin Cars of the Pennsylvania and Long Island Railroads" - Data Book Number 2. It shows PRR four-wheel wood cabin car Class NC with wood underframe adopted in 1893. It had an 11-foot wheelbase, 23-foot 6-inch length over end sills, 15-foot height over cupola, and 36-inch wheels. It also shows PRR four-wheel wood cabin car Class ND with steel underframe, introduced by Lines East in 1903 with 13-foot 6-inch wheelbase, 26-foot length over end sills, 13-foot 5-inch height over cupola, and 36-inch wheels. No similar cabooses are shown for LIRR.
I think a bobber caboose would be the most appropriate for your engine. I also have a model of LIRR #163 and think it is outstanding. MTH deserves credit for having made it.
MELGAR