Hey welcome Moose,
Mo and Gabel have given you good advice and mortises, tenons and pegs.
Here's more: Put aside your forstner bit. Buy some good auger bits, new or used min. 8" long, sharpen them if necessary. You can drill mortises into your hemlock with a 1 3/8" or 1 1/2" bit using a hand brace, or an elec drill. Score the outlines of the mortises w a knife and a steel straightedge 'cause hemlock can splinter coarsely. Also buy a 3/4" auger bit for pegging.
Buy some pegs from Northcott rather than making your own, with the time you you just saved practice some drawbore drilling in a few mock-up joints in waste wood but of same size you'll do in your frame. Draw your joints on paper, take your time on layout and double check. Then go ahead mark, score, drill, chisel and check. Do a few, you'll learn and get better w each. By the time you do your first one for real in your pergola frame it'll be much better than what you did 1/2 day earlier at the start of practice.
As Mo says "It would help to see the frame as a whole." Good to get it on paper and show it to someone qualified who can review w you and constructively advise. TF is a big wheel to re-invent! Be prepared to pay for this valuable information. Changes and corrections on paper are much faster and less expensive than in 8"x8" hemlock. An Architect we did some jobs for said many, many times, "A job well planned is a job half done." Us, being the hands-on guys didn't want to argue fractions w him, the point was well made and well taken.
Work safely and have fun too.
Steve