Okay, SIHR member Kevin Slater sent me what he has on this league, which is certainly incomplete due to the spotty nature of available newspapers. Some were certainly lost in fires in Haileybury. But there is some information available.
For 1905/06, I would hesitate to call it a hockey league, exactly. It seems more like a series of games between teams of the area. For many of the games, specific dates aren't even known, and there are likely some missing games. Home team listed last:
1905: New Liskeard 2-5 Haileybury
1905: Haileybury T-T New Liskeard
1905: Haileybury 2-7 New Liskeard
1906: Haileybury L-W New Liskeard
1906: New Liskeard 1-11 Haileybury
Feb 23, 1906: Haileybury 4-11 New Liskeard
Mar 20, 1906: Cobalt 1-10 New Liskeard
For 1906/07, there was a much more regular schedule, but we're still missing a number of games. All games were played in either Haileybury or New Liskeard, but it does not appear that the teams had regular "home" rinks (other than Haileybury or New Liskeard, that is).
Jan 27, 1907: Latchford 5-3 Cobalt (at Haileybury)
Feb 02, 1907: New Liskeard 5-2 Latchford (at Haileybury)
Feb 16, 1907: New Liskeard 4-3 Haileybury (at Haileybury)
Feb 18, 1907: Cobalt 5-3 Haileybury (at New Liskeard)
Feb 20, 1907: Cobalt 7-6 New Liskeard (at New Liskeard)
Feb 23, 1907: Cobalt 7-1 Latchford (at New Liskeard)
Mar 02, 1907: Cobalt 5-1 New Liskeard (at Haileybury)
There was going to be a championship series between Cobalt and New Liskeard, but results are unknown.