Yes, it's pretty standard to charge full adult price for a child, unless you can get a specific single parent deal. Some tour operators do single parent deals but only to certain hotels - when I was looking recently I noticed that a lot of hotels in Turkey offer SPDs. Think that was either with First Choice or Thomson so get some brochures and have a look (they'll state the SPD on the page), then ring the call centre and ask them - I was told by a travel agent that only the call centre can offer SPDs so you'll need to ring them direct. The single parent deal is usually that you pay full adult price, pay first child price for your child, plus the under occupancy supplement for only having one adult in the party, so in theory it should work out cheaper than paying for two adults. With regard to holiday villages, only the Holiday Village Costa Del Sol in Spain offers a single parent deal, so you could try getting quotes for there, otherwise it's a case of looking for ones where the prices are based on 2 people occupying the room so you at least won't get charged an under occupancy fee.
The other thing to do is shop around. As your DD is not of school age, go in term time and it'll be cheaper. Search all the websites you can think of and keep looking, so that when you spot a deal you'll know instantly and can buy it. The holiday villages are geared up for kids but so are lots of other hotels, so keep an open mind when looking. Last year I took my then 4yo DS to a Thomson family resort in Ibiza. We went in Sept so it was cheaper anyway, plus I booked via the Holiday Hypermarket website and saved £140 on what the travel agent had quoted me for exactly the same holiday. I also booked via a cash back website so ended up getting £34 cash back - not a fortune but it paid for the travel insurance! Never book via a travel agent without doing your research - while I was looking this year, every single holiday I was quoted for by a travel agent, without exception I could find the exact same holiday cheaper online.
Another thing you could consider is booking flights, transfers and accommodation separately. I was going to do that but left it too late and the flight prices rocketed.
This year (next week actually!) we're going to the Holiday village Flamingo Beach in Lanzarote. Before booking it I was looking for over a month - and when I say looking, I was literally browsing the websites every lunchtime at work and most evenings - then suddenly out of the blue, one day I was browsing Lanzarote hotels and it came up really cheap. Well not cheap, but very reasonably priced for a holiday village, iyswim. So I booked it - this was about 3 weeks ago, so I booked about a month before going. I checked the price online again last week and it's gone up by over £200 per person, so I got a bargain. I paid the same for 5yo DS as for me - as a single parent you just have to suck it up I'm afraid.
Give me a shout if I can be of any more help - I love looking for holidays!