ZebbyUK, you could transfer the shares into a stocks and shares ISA in her name and have the income from the shares reinvested (i.e. the dividends are used to buy more shares in the company paying the dividend).
These days dividends from stocks held in ISAs are not exempt from income tax, but growth in the value of the stock is exempt from Capital Gains Tax.
So she could cash some of the shares at age eighteen, say, without penalty.