Good info so far here.
On 300K hanging heater 'LOL'. The meter to your home is probably rated at 250,000 BTU/hour. 300K BTU/Hour is kind of like asking, "My new compressor takes 250 Amps on 220. What size wire should I run to my breaker?" The answer of course is, "it sort of don't matter'.
To the OP's question...even without a load calculation, I would feel very comfortable running 1 1/4" or somewhat comfortable running 1", because either will haul a lot of gas to 45-feet. 1" PE SDR 11 will flow 294,000 BTU's/Hour at 1/2" pressure drop at that distance. Now, you want to build some "safety factor" in that number for pressure losses due to fittings and such, plus headroom for the future...but that's going to be plenty big for your garage heater, regardless of your load calculation.
The difference in cost between 3/4", 1" and 1 1/4" PE is very small, really and you'll find that the vast majority of your cost is in labor and not material. I just bought 7000 feet of 2" PE this morning, for example, and it was only 80 cents a foot. Ditch costs are measured in dollars/foot, not cents/foot....if you get my drift.
And regarding the professional vs non-professional, that one hit pretty close to home. I've seen a lot of piping situations where too much money was spent because someone just "ball parked" a pipe size based on "gut instinct" and I've seen pipe that was undersized because someone felt it would be "good enough". And these people were "professionals". They just weren't "detail oriented" I guess, to maybe put the best spin on it.
Not a big deal to go 1 size too big if you only need 45 feet of PE. A little larger issue if it's 5 miles of 4" Schedule 40 coated steel.
Good luck. Bury it 18 to 24 inches deep and use a tracer wire. Probably work out well.
Phil