It's understandable. Lack of sleep can make anyone cranky and 7-months of poor sleep is enough to try anyone's last nerve. Equally, she could be struggling to cope and might need some help, possibly even medication.
We can't immediately tell if she has a problem and diagnosis by internet is rarely effective... but you are the best-placed person to know your wife and she seems to be getting angry enough to make you concerned it would be a good idea to try to give her some help.
First off, it's very likely your wife needs a regular break. Make sure she gets some 'me' time, if she has a hobby then try to encourage her to sign up to a club or regular meeting which does not revolve around children. Even if it's not at bedtime it's amazing how a bit of time out can really help recharge the batteries. Make sure you're doing your fair-share of things around the house too... I can't stress that enough and do it without being prompted.
It sounds a bit 'hippy' but at that age they're the perfect age to travel around forward-facing in a sling (I miss being able to use my traditional cloth sling, others are available!) Pop them in it and go for a walk to the park or the shops - 7-month-old's love to get out into the world and see what's going on from a daddy's eye-view and you can talk about the things that are going on. We used to love going out and you'd be amazed at the responses you get.
Second, it's worth investigating if your wife might have post-natal depression...
The main symptoms include:
- a persistent feeling of sadness and low mood
- loss of interest in the world around you and no longer enjoying things that used to give you pleasure
- lack of energy and feeling tired all the time
- trouble sleeping at night and feeling sleepy during the day
- feeling that you're unable to look after your baby
- problems concentrating and making decisions
- loss of appetite or an increased appetite (comfort eating)
- feeling agitated, irritable or very apathetic (you "can't be bothered")
- feelings of guilt, hopelessness and self-blame
- difficulty bonding with your baby with a feeling of indifference and no sense of enjoyment in his or her company
- frightening thoughts – for example, about hurting your baby; these can be scary, but they're very rarely acted upon
- thinking about suicide and self-harm
source: postnatal depression symptoms (nhs.uk)
... certainly the level of anger toward your child has been enough to make you uncomfortable, so it's worth looking out for other signs and seeking help if necessary. Postnatal depression is very common and is absolutely not an indication of failure, and there will be plenty of local resources and support groups who can help you.
Your question and profile don't indicate your location but if you want to share it then we as a community may be able to point you in the right direction.