My husband is in Basic Military Training right now and I need to file his taxes for last year, should I file them jointly even though we were only married this year?

If you did not get married until 2023 then you cannot file as married for 2022.   So ....when did you get married?  If you mean you got married in January of 2023---last month----no, you cannot file a joint return.  His 2022 return has to be filed as Single.

Next year when you file a 2023 tax return you can file a married joint return.  For 2022 you are each single and you each file a return as Single.   Or if you have children the one who had children might be able to file Head of Household for 2022.

You can request an extension for your spouse ---- later in March the form will be available to request an extension that would give your spouse until mid-October to file his tax return.   By April 18 he would need to pay estimated tax due-----IF he owes.  If he is getting a refund there is no problem with filing past the deadline.  If you do not owe or are getting a refund you have three years to file the tax return and get your refund.

If you were married in January 2023, you should prepare both returns separately with a filling status of single for each of you.  

You can go ahead and file your return as soon as you're ready to.  

However, you can prepare your husband's tax return, but he will have to sign it.  I recommend you file for an extension.  This will give you until October 18th, 2023 to file it.