No you can't do that (put PPL training through the business). Not in this case and not in most cases. You
must see a competent accountant.
The income may be taxable but if so then so will be the operating expenses (allowable against the income), and rest assured the expenses will exceed the income
The creation of a limited company doesn't in itself change the above position. It does clean it up but the Revenue doesn't like arrangements like this, where a ltd co. owns one plane, leases it to one customer... and don't ask me how I know
To create a business that will stand up for Revenue (and VAT, if applicable) purposes you need multiple customers, all at arm's length. The Revenue are on a crusade against everybody to do with boats, planes, horses.
The main scenario where a ltd co. is worth doing is where others fly it. Then, if somebody crashes it and creates a huge uninsured loss, the owner (you) should be protected. Provided you acted properly in your capacity as a Director