I think it's something to start in babysteps, get one thing done be pleased with yourself and then try the next.
So if you are feeling run down I would look around for a local evening course in yoga or some other gentle exercise, and then tell your dh that you will be doing that, and he will be on duty at that time (not babysitting, just being the primary carer for that hour or so). Just that small amount of time not being primarily a mum, and spending time with other people who do not see you first and foremost as a mum should really help, and exercise is really good for lifting your mood and helping you feel more together (I find it also helps me sleep, which I expect is still a problem with a 9mth old). Try and time it so it doesn't hit a feed, but at nine months your ds might get angry but he shouldn't suffer if your breast is not immediately available. Your dh will be fine too.
The other thing I would do is look to see if there are any activities for dads and toddlers at the weekend to send your dh off to with his dd. Only having one of them will still be a bit of a break for you and should help your dh to get to know his daughter. Things like tumble tots are a possibility, or perhaps a swimming session or rhythm type session if your dh (and dd) likes music.
Finally I would look to see if you can find a professional nanny or childminder to occasionally have one or both of your children, whether that is just for an hour every now and then, or on a regular basis. That might be in the day for you to generally recover, or in the evening to do things wit your dh, or both. This is not a luxury IMO, if you can afford sporting events, expensive watches etc then you can afford regular childcare and it is a perfectly reasonable thing to do (and not unusual).
Having two children with a small gap is utterly totally exhausting and you should not in any way be beating yourself up if you are feeling very frazzled. The plus side is once you are past the intense baby period it has lots of benefits. I have a 16mth gap between mine, and once the younger was two or so it really became a pleasure and so much less work than friends with bigger gaps because their needs were so similar (great for friendship, holidays etc).
The other thing that I would do right now is to start a food and drink diary, and check to see if you are feeding yourself enough of the right things. Breastfeeding (especially when coupled with looking after a toddler) is very energy intensive. Are you drinking enough on a regular basis? Do you have nice things to eat in the house that make you feel good in yourself? Things like having fresh orange juice, nice fruit and good snacks (nuts, carrots, granola bars) as well as making sure that you are sitting down and eating a good lunch (think plenty of protein) as well as obviously a good breakfast.
One thing I found very valuable when my two were little was having a long bath every night (I also used essential oils - mandarin is a good mood lifter). dh was in total charge at that time, and although it was just 45 mins or so it was important to me.
Personally I do agree with Xenia though. Going back to work restored a lot of balance in my life, and meant that dh and I returned to equal roles (something I really struggled with during maternity leave, being an independent sort of person).