Caring for the 11 month old will need to happen at that child's home. This gets you around the childminder regulations in childcare law.
Run it past HMRC Status Team.
Before contacting them make sure you know:
If the days you will be caring for the child are the same each week, or will vary.
If you have any obligation to provide the care - can you turn down requests?
How many other clients you have for whom you do the same/similar thing.
How many other clients you anticipate having once the business picks up.
It makes most sense to me to sort all the tax as i will be doing it for the group anyway.
It is not as simple as that. If it is a job, as a nanny you are most likely to be an employee. It's a matter of what the facts indicate, such as amount of control the parent has over you. There are numerous factors which HMRC will take into account, so talk to the status team.
I'm the "emergency nanny" for a different friend with a long commute
That is very ad-hoc work, so more likely to be self employment, though may depend how long each assignment lasts.
Is £5ph about right? I'll collect the other dc then take them both to play group, provide snacks and drop her home (rural area, car essential although i do normally make the effort and walk, it's a couple of miles)
Sounds low even for a NWOC (nanny with own child). You need to consider how much you would be spending out on advertising (you need to make it look like a business if HMRC are to agree it is a business, not employment), class 2 national insurance, class 4 national insurance (if profits £7755 or higher), income tax (if your total income from all sources totals over the personal allowance), liability insurance, equipment, business use motor insurance / specialist motor insurance for nannies.
You MUST NOT go to your home. If playgroup was not on, you must go somewhere else, or back to the child's home. Do not confuse things by going to your house, as that can then become childminding with requires registration. Sure there are time rules within legislation but I would avoid the issue completely by providing the service from the child's own home.
we were going to go through nannytax or somesuch
You can contact nanny payroll services for advice. Perhaps have a chat to them with regard to emergency nannying and if caring for this 11 month old would fit with being emergency/temp, or not.
Toddler group wise, look into insurance requirements. Pre-school Learning Alliance has information about starting a toddler group, plus can provide an insurance quote. Insurance for toddler group is also available from Morton Michel.
Consider your costs: advertising, rent, heating/lighting (if not included in rent), equipment, snacks. Keep records of all expenditure and income.
This pdf looks useful. It is for groups in Scotland but much will apply elsewhere.