Merk this happened to me at 9+3 pretty much exactly as you describe and the resulting baby is currently on my lap trying to stop me typing on my phone so try not to panic, which I know is near impossible. If you search there are loads of stories online of early pregnancy bleeding (some really bad) resulting in healthy babies which I found reassuring to read when it happened to me.
Get yourself on the sofa with a box set and a supply of drinks and snacks and don't move for the rest of the day. There is no point walking around to make it worse when you actually want it to stop! And also don't panic if you can't find a heartbeat with the Doppler as it's far too early to reliably find it every time and some MW's even struggle to find it at 16 weeks.
It also happened to me on a weekend and I had to go through the torture of waiting until EPU opened on Monday morning. I couldn't self-refer to mine (I think some you can) so I phoned my named MW first thing Monday morning and she arranged for a scan Monday lunchtime.
EPU shouldn't want to see the towel unless it is unusual in some way, they will want to know about the colour, whether there are any clots, quantity, duration and any accompanying pain. I got the impression that brown blood isn't seen as a potential problem so if you want to get a scan make sure you emphasise how red it was.
I would only go to A&E if you have symptoms of ectopic (which you definitely haven't if you've already had a scan showing a baby in the right place?) and phone your out-of-hours GP number if bleeding gets heavier or is accompanied by cramps and they will get someone to assess/advise you over the phone, although all they can really offer is pain relief. NHS Direct were useless IMO and not worth bothering with for early pregnancy.
You've seen a good strong heartbeat already so I'm sure this is just one of those unexplained incidents which don't indicate a problem. 