I'm going to give you information from the index card in the "War of 1812 Pension Application Files Index":
Soldier:Alvin Wheeler Service:Capt. Alexander Gibson Co., OH Mil. S.O.:5908 S.C.:6408 Bounty Land Warrant:574-80-50 and 27698-80-55
If you've got some money to put into the research, you can get a copy of Alvin's Pension File and his compiled service record from the National Archives.(Some researchers treat each as a different task and charge accordingly:i.e. copying the pension file is one task and copying whatever's in the compiled service record is another.)You can ask (and pay) the National Archives staff to do the job or you can hire an independent (non-employee) to do the job. Just make sure that if you're hiring an independent researcher that you hire one living in or as near to Washington D.C. as possible, otherwise you could end up paying quite a bit for "commuting cost."
BTW, you didn't say that your Alvin Wheeler moved down into Indiana, but my wild guess is that you're going to tell me he did.I searched Land Patents at http://www.glorecords.blm.gov/http://www.glorecords.blm.gov/ and did not find any issued to Alvin Wheeler in Ohio.But, on a hunch, I checked to see if he might have moved into Indiana (a common place to go from Ohio) and found two patents issued to Alvin Wheeler in Indiana.Try your hand at searching for them.If you can't find them, let me know and I'll give you detailed instructions on how to find them.