Hello there,
The basic cover that you can take out is life, which usually comes with terminal illness cover which means that it will pay out on first death if you are given less than a year to live. Although this tends to be cheaper, you need to think about how much income you would need if one of you were to die, not just based on the mortgage cost, but also the lost income etc. You may wish to think about death and critical illness, which will pay out if something happens which seriously affects your quality of life. A financial advisor will go through what you would need if one of you were to die, or what you would need to support your daughter if both of you were to pass. You should then review your cover every year in line with your change in circumstances.
Although you can get some very cheap quotes for life cover, I would reccomend going with a reputable provider, such as Legal and General or Norwich Union as many companies will find an excuse not to pay out, for example if they discover a hereditary illness in your family which you were unaware of. This is the last thing you need if you (heaven forbid) have to cope with the death of a partner.
Getting a quote direct from a provider is cheaper, but if you get one through a financial advisor they can go through a review with you and you can get the most suitable cover. I would approach another fa, you shouldnt have to wait for anyone!
Hope this helps
Good luck!!