Too many unknowns to advise, but the big worry is that overdrafts can be expensive and there's always the risk that the bank will recall it and you'll have to pay it off more quickly than is comfortable.
Whether it is a worry depends on how much it is and how much it costs. If it's not very much, you can get the same cashflow help by putting your spending on a credit card and paying it off in full every month without fail. Therefore the money that would have taken you into overdraft remains in your current account until after payday and you could even earn a bit of cashback with the right card.
But you should also honestly think to yourself whether there are any costs you can cut out of your 'not lavish' lifestyle.
There are plenty of things that people spend on that they think as normal/necesscities, that are actually luxuries, that the could cut back on. Things like food and drink out of the house, can cost hundreds of pounds a month if you do it every day, so plenty of scope to cut back by taking a packed lunch most of the time. Also what are you spending on grocery shopping. Some people spend 2 or 3 times more than others do, so again, possible scope to cut back if you are a high spender.
Also check you have cut all your regular costs as much as possible and shop around and use voucher codes and cashback sites too. The difference between doing all this and not can also be hundreds of pounds a month between a wasteful and a careful approach.
You say you don't want to work more, due to lack of time with your DD, but if you've never really thought about budgeting before, it could be far more productive to spend some time getting a good handle on your finances, to see if you are leaking money anywhere
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