Northern Ireland has said it will also follow Wales and Scotland in offering young children the vaccine.
Our health correspondents Smitha Mundasad and Philippa Roxby answer some of your questions:
The benefits of getting a vaccine are likely to apply mainly to a future wave of infection.
And we don't know for certain when the next wave will occur or how severe it will be.
Most healthy children do not get severely ill from Covid-19 but some do.
With this in mind families may decide to take the paediatric dose for their 11-year-olds while their children are eligible - as this will provide some protection relatively quickly.
Experts are advising children to have their vaccines in the school holidays to avoid disruption to their education from any flu-like side effects of the jab.
Covid vaccines may not have been around of many years but they have been heavily scrutinised from the moment they were developed.
Safety monitoring systems set up around the world - including the UK's Medicines and Healthcare products Regulatory Authority - collect and share the very latest information from the hundreds of millions of people who have been vaccinated against Covid so far.
This shows most side-effects are mild and short-lived - such as pain at the injection site or a fever. Some more serious side-effects, including inflammation of the heart muscle, are rare.
Looking at the history of other vaccines, most side-effects become apparent within the first few months of having a jab. And side-effects need to be weighed against the harms of Covid infection.
Some medical conditions put children at higher risk of getting severe Covid. This includes chronic heart conditions and in some cases congenital heart disease.
If your child's illness is on the at-risk list - and it would be best to check with her GP or specialist - then the advice is she should be offered two doses of the vaccine to help protect her from severe disease.
Otherwise healthy children are at lower risk of severe Covid but a small number will still get very unwell with it.
Natural immunity arising from prior infection will contribute towards protection against future infection and disease.
But how strong that protection is can vary highly from person to person.
And some studies suggest protection against severe disease is more consistently strong from vaccines.
Getting vaccinated - even if someone has had Covid-19 already - means they are more likely to be protected for longer.
The potential benefits from vaccination apply mainly to a future wave of infection; the more severe a future wave, the greater the likely benefits.
In terms of side-effects, in the United States, fewer than two cases of vaccine-related myocarditis have been reported per million doses.
The UK's vaccine advisory body has recommended the jab for your daughter but there's no major rush for her to get it.
Children are at extremely low risk from the virus and if she has recently been infected, she will have some in-built protection already.
She would have to wait for four weeks after her last infection before having a jab in any case.
Two vaccine doses on top that would mean she would be well-protected if there was a new variant or a new wave of infections this winter.
The vaccines aren't very good at stopping infections but they do provide strong protection against serious disease, and that lasts for some time.