The toilet needs to be anchored to the flange. If there isn't enough room to set the toilet in the proper position over the flange then you have a couple of choices...get a different toilet or move or change the flange. Offset flanges are not often looked upon as a good choice.
Are you saying you only have 11" or is it 13"? If 13", you don't need a new toilet, but you'll have a little bigger (by 1" gap) than the manufacturer designed, but that will have no performance impact. If it is 11", you have to look carefully at the specs, you might make a 12" one fit, but it very much depends on the brand and model.