DD is nearly 8 months and after the first couple of months (while I was just finding my feet with this motherhood malarkey), I had to endure the curse that is school holidays which puts a stop to 90% of groups around here. Personally, I hate staying indoors and as I was concerned about a risk of PND (previous history of depression, family history of PND), I was keen to make sure I got out & about as much as possible, if only to the park & shops during the school holidays. Once DD was 3 1/2mo, school had restarted and so had the groups (none of the ones I go to are Surestart supported).
I take DD to 2 groups Monday & Tuesday (morning & afternoon groups unless I'm taking DD to see the HV one afternoon), 1 Wednesday morning, 1 Thursday afternoon & 1 Friday morning. I have to say that I believe that going to the groups has been beneficial to DD's development as she was the youngest at a few of the groups for quite a long time and she seems to like copying the older babies. Personally, I don't think I've come across any competitive mums in any of the groups (although that could mean that I'm the competitive mum 
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If you are interested in getting out with your DD, good places to find out about Mother & Baby/Toddler groups (IME, toddler groups don't seem to mind younger attendees) seem to be your local library, churches, community centres, post offices (notice board), and possibly your health visitor/health centre. One of my local supermarkets has a notice board opposite the baby changing room which has details for some baby groups. Also, in my area, one mum has set up a Facebook group for local mums to share info about groups so everyone can find out what's going on on any one day, even just which days the local toy libraries are open. Maybe someone might have done the same things in your area/country?
Different groups I've been to with DD:
Breastfeeding support (the only one which didn't close for the summer hols - my saviour!) - my local one is a good chance for mothers to get together for a natter and have tea & biccies and ignore the LOs playing on the floor as much as possible as well as share advice,
Music group (singing & dancing, with a break for snacks & drinks in the middle),
M&B/T groups at local church (toys & craft for LOs, free tea/coffee & biccies for Mums),
Health Centre M&B group (marshalled by nursery nurses who got my back up a few times),
Language & Play group at local library (bit of craft, followed by a story and a sing song).
All of these groups have been free (apart from the odd biccie donation & some no obligation spare change in the church group box). There's also loads of paying groups I could have gone to (except I'm tightfisted and begrudge £4.50 an hour when I'm on maternity pay). Pretty much, if you want to take your DD out somewhere, you should be able to find something to suit you pretty easily.
HTH