Or have I got this wrong?
- basically yes. The standard procedure is to continue the take-off at or above V1. That said, it is always the Captain's call to deviate from this norm, although he/she needs to get it right if so and will be in conflict with published procedures leading to potential disciplinary actions.
As I said earlier, any Perf Category 'A' a/c should be able to continue at or above V1 and indeed, as you ask, below V2, although V2 is set as to be normally reached just after rotate.