A prop strike is unlikely, as Fox says. It's a bit less of an angle than getting someone to hold up the tail 'till a prop tip touches the ground, as on a take off run on a rough field the undercarriage will be flexing and the ground will be uneven; undercarriage compressed, wheels in dips in the ground, prop in line with a hump.... it will strike at the lesser angle, but probably still a lot less than you think.
I have flown a Tiger Moth but most of my t/w experience is in the Chipmunk. On that aeroplane it's surprising how hard a forward push you need to get a notable tail-high attitude on the t/o roll.
I have taken off in the Chippy 3-point, but as has been pointed out you will become airborne on the back of the drag curve. For soft field, better to get the tail up early for good acceleration then hoink it into the air early; it'll still be on the back of the drag curve but you'll get out of the mud more quickly. Then you fly just above the ground accelerating in ground effect and gradually reducing the AoA until you 'feel' the wings come to life on the front of the drag curve (easy in a Chippy - it 'talks to you' through the stick). then climb away as normal.
I don't know if the above applies to the Tiger, but I'd be surprised if it doesn't.