Forgot to say - she would need a domain (from 5 to 10 pounds, typically for a .co.uk, .org.uk, or .me.uk) to be able to use the hosting at Heart, but there's no penalty for registering one with any firm, and making a transfer.
Given you may not want home address details out in public (the 'WHOIS' information) you can register a .uk domain and request that 'whois' details are withheld (this means that a lookup at www.nic.uk would not show your home address). All registration firms should offer this, though it is sometimes 'hidden away' on their registration forms.
A separate firm, www.name.com offers similar 'whois' privacy for free, and they offer a range of domain names, perhaps the cheapest being .info, at about $4 for the first year.
Alternatively, you could use www.123-reg.co.uk (which has a deal on until the end of the month) and is offering .info domains for 88p (offer code is info88 ) - just make the registrant DH and perhaps put address of DH's company, if that's preferred/acceptable, if you don't want home address used.
After 8 months, if DD is still keen, transfer the domain to name.com for a low 'transfer in' fee, and that will bump up the expiry date by a year. HTH.