Rawalpindi is not necessarily as safe as it's sister, Islamabad. Islamabad has higher foreign tourist traffic, and thus has become accustomed to it, however foreign tourists are somewhat rare in Rawalpindi. Pakistan on the whole is not recommended to lone young female travellers, however Pindi is relatively safe for larger groups of females, or mixed gender paired-travellers. For female travellers, it is highly recommended to purchase a shawl upon arrival in Pakistan even better to bring one over on your flight, for airport arrival purposes. It is not necessary or expected for you to wear this on your head at all times, however to avoid unwanted attention, and gain local respect, cover your chest with this shawl i.e. drape it across your neck. Also attempt to purchase/wear a long shirt/top, that covers your backside region - this again, will draw away unwanted attention.
Avoid flashing large amounts of cash around - Rs 1000 notes are commonplace, however the haggling process is often easier when you show the limited cash you have e.g. "I only have Rs 200 on me". Keep your larger notes on the inside, and only allow small notes to be seen, for example, when paying taxi drivers, purchasing items, etc.
Do not feel compelled to give money to all beggars, not matter how young or needy. Of course exercise discretion, and it not unacceptable to give them money, however, the beggars are regulars in Pindi, and have their regular locations, and are known to beg in the same place, everyday - with a new outfit each day.